Step Up Learning Solutions

Table of Contents
Parts of Speech............................................................................................................................ 4
Nouns .......................................................................................................................................... 4
Pronoun ...................................................................................................................................... 7
Adjective .................................................................................................................................. 11
Verb ........................................................................................................................................... 13
Adverb ...................................................................................................................................... 15
Conjuctions ............................................................................................................................. 16
Interjection ............................................................................................................................. 17
Preposition .............................................................................................................................. 17
Vocabulary .................................................................................................................................. 21
Common Root Words ........................................................................................................... 21
Affixes ....................................................................................................................................... 23
Suffixes .................................................................................................................................... 24
Commonly Confused Words................................................................................................... 26
Idioms .......................................................................................................................................... 33
Subject Verb Agreement ........................................................................................................ 37
Punctuation ................................................................................................................................. 44
Active / Passive Verb Forms .................................................................................................. 53
Statement & Courses of Action ............................................................................................ 60
Syllogism ..................................................................................................................................... 62
Blood Relations .......................................................................................................................... 69
Analogy ........................................................................................................................................ 72
Coding & Decoding ................................................................................................................... 75
Data Sufficiency ........................................................................................................................ 78
Data Interpretation .................................................................................................................. 80
Percentages and Averages ..................................................................................................... 87
Ratio and Proportion ................................................................................................................ 96
Simple Interest and Compound Interest ......................................................................... 106
Speed, Time & Distance........................................................................................................ 115
Time and Work ........................................................................................................................ 122

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 Verbal Ability

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Verbal Ability

Parts of Speech

Every single word belongs to one of the eight word groups of parts of speech

1. Noun 2. Pronoun

3. Adjective 4. Adverb

5. Verb 6. Prepositions

7. Conjunctions 8. Interjections

Nouns
A noun is a word used to name a person, animal, place, thing and abstract idea.
A noun can function in a sentence as a subject, a direct object, an indirect
object, a subject complement, an object complement, an appositive, an
adjective or an adverb.

There are four kinds of nouns:

• Common Nouns
• Proper Nouns
• Concrete Nouns
• Abstract Nouns

A. Common Noun

A common noun names a class of similar things (chair, box), and not an
individual member of a specified group of people or things. We do not capitalize
the first letter of a common noun unless it is the first word in a sentence.

Common nouns are names of people, things, animals and places, etc.

• People – aunt, boy, butcher, carpenter, cousin, father, girl, lady, man,
mother, tailor, woman
• Things – bicycle, book, car, computer, dress, hammer, key, pencil, ship,
table, vase, wallet
• Animals – armadillo, baboon, bee, caterpillar, cow, dog, eagle, fish,
monkey, pig, snake, turkey

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 • Places – airport, beach, bullring, cemetery, church, country, hospital,
library, mall, park, restaurant, zoo

B. Proper Noun

A proper noun is a special name of a person, place, organization, etc. We spell a

proper noun with a capital letter. Proper nouns also refer to times or to dates in
the calendar.

We can use plurals for proper nouns in exceptional cases.

▪ There are three Johns in my class.

We can also use the, an, or a for a proper noun in special circumstances.

▪ This is no longer the London I used to live in.

Proper nouns are names of people, places, organization, etc.

▪ People – Ali Baba, Barack Obama

▪ Places – Downing Street, Museum of Modern Art, Sahara Desert
▪ Things – Financial Times, Eiffel Tower
▪ Organization – International Labour Organization, Red Brigades, United
Nations
▪ Animals – King Kong, Lassie
▪ Times and dates – Saturday, April

C. Concrete Noun

A concrete noun is something we see or touch. It is the opposite of an abstract

noun. There are countable concrete nouns and uncountable concrete nouns.

▪ Countable: teacher (people); valley (place); deer (animal); comb (thing)

▪ Uncountable: water (liquid); steam (gas); copper (substance)

D. Abstract Nouns

An abstract noun is a quality or something that we can only think of rather than
as something that we can see or touch, e.g. beauty, courage, friendship,
intelligence, truth. We can form abstract nouns from common nouns (child –

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childhood); from verbs (know – knowledge); and from adjectives (happy –
happiness).

Countable & Uncountable Nouns

Countable nouns (also called count nouns) are nouns that can be counted (e.g.
oranges). Uncountable nouns (also known as non-count or mass nouns) are
amounts of something which we cannot count (e.g. sand).

The noun is countable:

1. if we can use the indefinite artice a/an before it.

▪ I own a car. / I play with an ostrich.

2. if we can use the word 'many' to describe it.

▪ She has many friends.

3. if we can express its quantity by using a number before it.

▪ I have five apples.

4. if it takes on singular as well as plural forms.

▪ an orange / some oranges / fifty oranges

The noun is uncountable:

1. if a/an is not normally used in front of it.

▪ He is eating some rice. (NOT: He is eating a rice.)

2. if the word much can be correctly used with it.

▪ How much rice have you eaten?

3. if it is not possible for us to count it. However, we can make it countable by

having a quantity for it.

▪ I have just bought two cartons or litres/liters of milk. (NOT: I have just
bought two milk.)

4. if it takes only a singular form.

▪ some ice / some ink / some soup

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Pronoun
A pronoun is a word that replaces a noun or a group of words used as a noun. It
acts as a substitute for a noun.

Pronouns are classified into 8 different categories as follows:

A. Personal Pronoun

Personal pronouns refer to the speaker or the speakers(first person), those

spoken to (second person) and those spoken about(third person).

Pronouns which substitute nouns which refer to inanimate objects are called
impersonal pronouns.

Singular Plural Singular Plural

Subject pronouns Possessive pronouns

I we my Our

You you your your

He they his their

She they her their

It they its their

Object pronouns Possessive pronouns

Me us mine ours

You you yours yours

Him them his theirs

Her them hers theirs

It them

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B. Relative Pronoun

These pronouns join dependent clauses to independent clauses. They are who,
whose, whom, which and that.

We use that and which in almost the same way as we use who, but they refer to
things, not people. There is a difference in using which and who. After which, we
can use a verb, a pronoun or a noun. After who, we usually use a verb.

Using which

▪ That was the camera, which cost five hundred dollars. (Before verb)
▪ That was the camera, which he bought. (Before pronoun)
▪ That was the camera, which John liked. (Before noun)

Using who:

▪ Who lives in that haunted castle? (Before verb)

▪ That is the man, who is my dad's best friend. (Before verb

C. Indefinite Pronoun

Indefinite pronouns are pronouns that do not point out specifically. We use
indefinite pronouns to refer to people or things without saying exactly who or
what they are. We use pronouns ending in -body or -one for people, and
pronouns ending in -thing for things.

D. Reciprocal Pronoun

There are only two reciprocal pronouns: each other, one another. The
reciprocal pronouns are used to express a relationship in which something is
done by each of two or more parties towards the other or others. They refer
mostly to people, but they can also be applied to animals or things. A plural
subject is always used as more than one person or thing are involved.

Each other is usually used when writing or speaking about two people or things.
For more than two people or things, one another is generally used.

▪ Their parents often argue with each other.

▪ The few puppies chased one another across the field.

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Reciprocal pronouns as objects of a verb.

▪ This is the tenth year that Jack and Jim have known each other.
▪ Before they began talking, they bowed to one another.

Reciprocal pronouns following a preposition(at, with).

▪ No one knows why they are shouting at each other.

▪ They realized it would be much easier if they all cooperated with one
another.

Reciprocal pronouns have the possessive case.

▪ The two old monkeys are seen scratching each other's heads.
▪ When the two groups met, they started shaking one another's hands.

E. Demonstrative Pronoun

The four common demonstrative pronouns are this, that, these, those. We use
them to indicate the person, thing or place referred to, with this used to refer to
someone or something nearer (that is, nearer to the person speaking) while that
refers to the farther one. If there is more than one person, thing or place
referred to, we use these, which is the plural of this. Those is the plural of that.

F. Reflexive Pronoun

Reflexive pronouns are those pronouns formed by adding ‘ –self’ to singular and
‘–selves’ to plural possessives to produce the following: myself, yourself, herself,
himself, itself, oneself; and ourselves, yourselves, themselves.

Reflexive Pronouns Singular Plural

First person I : myself We : ourselves

Second person You : yourself You : yourselves

Third person He : himself They : themselves

She : herself They : themselves

It : itself They : themselves

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G. Possessive Pronoun

The possessive pronouns are the possessive forms of personal pronouns. We use
the personal pronouns in the possessive case to express possession. A
possessive pronoun is able to stand on its own as subject, object, etc.

Possessive pronouns

Singular Plural

Mine Ours

Yours Yours

His Theirs

Hers Theirs

Possessive pronouns can be used as either subject or object:

▪ Yours has weeds all over. (Subject)

▪ Your dog has bitten mine on the stomach. (Object)

We do not insert an apostrophe in possessive pronouns (especially,

yours, his, hers, its, ours, theirs) that express ownership.

▪ This slice of pizza is yours.

▪ It is licking its paw.
▪ Whose footprints are these?

H. Interrogative Pronoun

Interrogative pronouns are used in asking questions. There are five of them, all
of which begin with wh-: who, whom, whose, which, what. Who is used for
people while which and what are used for things. These pronouns do not have
gender.

Using who:

▪ Who are you shouting at?

▪ Who is that person?

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Using whom:

▪ Whom are you staying with?

▪ Whom do you wish to speak to?

Using what:

▪ What is your address?

▪ What are you going to do?

Using which:

▪ Which of these colours do you like?

▪ Which do you think is better?

Using whose:

▪ Whose is that car?

▪ Whose are those children?

Note - Who is the subject pronoun while whom is the object pronoun.

Adjective
A. Adjective of quality

Descriptive adjectives are the most numerous of the different types of

adjectives. These adjectives describe nouns that refer to action, state, or quality.

▪ dangerous chemicals
▪ green vegetables
▪ a square box
▪ a big house
▪ a tall tree
▪ a cold morning
▪ a true story
▪ English language
▪ Mediterranean country.

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B. Adjective of quantity
An adjective of quantity tells us the number (how many) or amount (how
much) of a noun.

▪ He has eaten three apples.

▪ I don’t have much money.
▪ There is so much wine for the guests.
▪ This long, thin centipede has many legs.

C. Demonstrative adjective
A demonstrative adjective (this, that, these, those) shows the noun it modifies is
singular or plural and whether the position of the noun is near or far from the
person who is speaking or writing. A demonstrative adjective also points out a
fact about the noun.

▪ This red balloon is mine and those three yellow ;ones are yours.
▪ This cute baby is his brother. That cute baby is his sister.
▪ These two fat cats have tails, but that thin cat doesn’t have a tail.

D. Possessive adjective
A possessive adjective expresses possession of a noun by someone or
something. Possessive adjectives are the same as possessive pronouns. All the
possessive adjectives are listed in the following table:

Singular Plural

My Our

Your your

His their

Her their

Its their

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Verb
Verbs are a necessary component of all sentences. Verbs have two important
functions: Some verbs put stalled subjects into motion while other verbs help to
clarify the subjects in meaningful ways.

A. The transitive verb

A transitive verb must have an object. Without an object, it does not convey a
clear meaning.

Example - He bought.

The question inevitably arises: What did he buy? No one in the world knows the
answer to this question as there is no direct object to tell us what he bought.
The meaning becomes clear when an object is added: He bought a cake. Now
everyone of us knows what he bought.

The subject (he) performs the action: bought. The object of the action verb
bought is cake.

A transitive verb may take an indirect object. An indirect object is something or

someone to whom or for whom the action is carried out.

He bought her a cake. = He bought a cake for her.

She is reading grandma the news. = She is reading the news to grandma.

In the first sentence, the indirect object is her as it is for her that the cake was
bought. In the second sentence, the indirect object is grandma as it is to her
that the news was read. The indirect object usually comes before the direct
object as shown in above two sentences.

B. The intransitive verb

An intransitive verb does not have an object. Without an object, the meaning is
not affected.

Example: She smiles. / The dog is barking. / Their plane has already taken off.

All the verbs (smiles, is barking, has taken off) are intransitive as they do not
need an object to make the meaning clear.

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Example: The villagers caught a boar yesterday, but it escaped this morning.

The verb caught is transitive as it has the direct object boar. The other verb
escaped is intransitive since it is not followed by an object.

Moods of the Verb

Mood is a form of a verb that indicates the attitude of a speaker or writer. Verbs
have three moods that express:

▪ simple statement of a fact (indicative mood),

▪ command (imperative mood), or
▪ imagination or wish (subjunctive mood).

A. Indicative mood - The indicative mood of a verb is the most frequently used
simple statements of fact and in questions.

▪ The meal is delicious.

▪ She drives to work every working day.
▪ Have you done your homework?
▪ Do you believe in Ghost?

B. Imperative mood

The imperative mood of a verb is used to express a command or give an order.

When written, the imperative is accompanied by an exclamation mark (!) at the
end of the sentence or word. The subject of imperative statements is understood
to be the second person. It therefore uses the second-person verb.

▪ Wait here!
▪ Pay attention!
▪ Leave me alone!

The imperative may also be used to express an instruction without the use of the
exclamation point to signify it's less emphatic.

▪ Get it done by today.

▪ Close the door behind you.
▪ Put it over there.

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C. Subjunctive mood

The subjunctive mood of a verb expresses what is imagined, wished, possible or

not necessarily real or true. The subjunctive form uses the past tense of the
verb be which is were, not was. Remember that in using the subjunctive, wereis
used for all persons.

▪ I wish I were an astronaut.

▪ You behaved as though you were the only one with that ability.
▪ Would she go supposing she were invited?

We use the subjunctive mood when making hypothetical statements beginning

with if.

▪ If he were alive, he wouldn't be happy with what you are doing

▪ If I were you, I wouldn't do a stupid thing like that.
▪ If she worked hard, she could go to university.

Adverb
An adverb can be added to a verb to modify its meaning. Usually, an adverb tells
you when, where, how, in what manner, or to what extent an action is
performed.

A. Adverbs of Time - Adverbs of Time tell us something about the time that
something happens. Adverbs of Time mainly modify verbs. They answer the
question "when?" or the question "how often?"

▪ Press the button now.

▪ We sometimes watch a movie.
▪ I tell him daily.

B. Adverbs of Place - They answer the question "where?". Adverbs of Place

mainly modify verbs.

▪ Daisies grow everywhere.

▪ I did not put it there.

C. Adverbs of Manner - Adverbs of Manner tell us the manner or way in which

something happens. They answer the question "how?"

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 ▪ He passed the re-sit easily.
▪ The lion crawled stealthily.

D. Adverbs of Degree - Adverbs of Degree tell us the degree or extent to

which something happens. They answer the question "how much?" or "to what
degree?". Adverbs of Degree can modify verbs, adjectives and other adverbs.

▪ That is the farthest I have ever jumped.

▪ He boxed more cleverly.

Conjuctions
Conjunctions are used to join words or groups of words together. Conjunctions
can be categorized into one of three groupings:

A. Coordinating Conjunctions

Coordinating conjunctions are the ones that spring to mind when people think
about conjunctions. They include and, but, or, nor, for, so, and yet.

Coordinating conjunctions are used to join individual words, phrases, and

independent clauses.

Coordinating Conjunctions Joining Individual Words:

▪ Jamie, Adam, and Lee arranged to meet by The Bull at 7 o'clock.

▪ It is a small but practical kitchen.

Coordinating Conjunctions Joining Individual Phrases:

▪ The finance manager and his new deputy from Holland will notify you
when the report is ready to send.
▪ John or his new deputy from Holland will notify you when the report is
ready to send.

Coordinating Conjunctions Joining Individual Clauses:

▪ A little sincerity is a dangerous thing, and a great deal of it is absolutely

fatal. (Oscar Wilde)
▪ We are all in the gutter, but some of us are looking at the stars. (Oscar
Wilde)

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 ▪ History will be kind to me, for I intend to write it. (Winston Churchill)

B. Correlative Conjunctions

Correlative conjunctions appear in pairs. For example, either...or, neither...nor,

whether...or, and not only...but also.

C. Subordinating Conjunctions

Subordinating conjunctions include: after, although, as, because, before, if,

once, since, than, that, though, till, until, when, where, whether, and while.

They are used to show the relationship between an independent clause a

dependent clause.

▪ Keep your hand on the wound until the nurse asks you to take it off.
▪ Personally I'm always ready to learn, although I do not always like being
taught. Sir Winston Churchill (1874-1965)
▪ We can't all be heroes because somebody has to sit on the curb and clap
as they go by. Will Rogers (1879-1935)

Interjection
An interjection is a word which shows emotion. It is not grammatically related to
the rest of the sentence. Interjections are often placed at the beginning the
sentence.

▪ Hey! Get off that floor!

▪ Oh, that is a surprise.
▪ Good! Now we can move on.

Preposition

A preposition describes a relationship between other words in a sentence. In

itself, a word like "in" or "after" is rather meaningless and hard to define in mere
words.

A. Prepositions of Time: at, on, and in

We use at to designate specific times.

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 ▪ The train is due at 12:15 p.m.

We use on to designate days and dates.

▪ My brother is coming on Monday.

▪ We're having a party on the Fourth of July.

We use in for nonspecific times during a day, a month, a season, or a year.

▪ She likes to jog in the morning.

▪ It's too cold in winter to run outside.
▪ He started the job in 1971.
▪ He's going to quit in August.

B. Prepositions of Place: at, on, and in

We use at for specific addresses.

▪ Kate lives at 833 Collins Street in Mebourne.

We use on to designate names of streets, avenues, etc.

▪ Her house is on Collins Street

And we use in for the names of land-areas (towns, counties, states, countries,
and continents).

▪ She lives in Melbourne

▪ Melbourne is in Australia.

C. Prepositions of Movement: to and No Preposition

We use to in order to express movement toward a place.

▪ They were driving to work together.

▪ She's going to the dentist's office this morning.

Toward and towards are also helpful prepositions to express movement. These
are simply variant spellings of the same word; use whichever sounds better to
you.

▪ We're moving toward the light.

▪ This is a big step towards the project's completion.

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With the words home, downtown, uptown, inside, outside, downstairs, upstairs,
we use no preposition.

▪ Grandma went upstairs

▪ Grandpa went home.
▪ They both went outside.

D. Prepositions of Time: for and since

We use for when we measure time (seconds, minutes, hours, days, months,
years).

▪ He held his breath for seven minutes.

▪ She's lived there for seven years.
▪ The British and Irish have been quarreling for seven centuries.

We use since with a specific date or time.

▪ He's worked here since 1970.

▪ She's been sitting in the waiting room since two-thirty.

E. Prepositions with Nouns, Adjectives, and Verbs.

Prepositions are sometimes so firmly wedded to other words that they have
practically become one word. This occurs in three categories: nouns, adjectives,
and verbs.

Nouns and Prepositions

approval of fondness for need for
awareness of grasp of participation in
belief in hatred of reason for
concern for hope for respect for
confusion about interest in success in
desire for love of understanding of

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 Adjectives and Prepositions
afraid of fond of proud of
angry at happy about similar to
aware of interested in sorry for
capable of jealous of tired of
careless about familiar with worried about

Verbs and Prepositions

apologize for give up prepare for
ask about grow up study for
ask for look for talk about
belong to look forward to think about
bring up look up trust in
care for make up work for
find out pay for worry about

F. Idiomatic Expressions with Prepositions

▪ agree to a proposal, with a person, on a price, in principle

▪ argue about a matter, with a person, for or against a proposition
▪ compare to to show likenesses, with to show differences (sometimes
similarities)
▪ correspond to a thing, with a person
▪ differ from an unlike thing, with a person
▪ live at an address, in a house or city, on a street, with other people

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Vocabulary

Many English words are formed by taking basic words and adding combinations
of prefixes and suffixes to them. A basic word to which affixes (prefixes and
suffixes) are added is called a root word because it forms the basis of a new
word. The root word is also a word in its own right.

In many cases, knowing the root word will be enough to help you decipher the
meaning of a word in a sentence. The root and its meaning will at least give a
partial understanding of a more complete definition.

Common Root Words

Common Latin Roots

Latin Root Definition Examples

Ambi Both ambiguous, ambidextrous

Aqua Water aquarium, aquamarine
Aud to hear audience, audition
Bene Good benefactor, benevolent
Cent one hundred century, percent
Circum Around circumference, circumstance
contra/counter Against contradict, encounter
Dict to say dictation, dictator
duc/duct to lead conduct, induce
Fac to do; to make factory, manufacture
Form Shape conform, reform
Fort Strength fortitude, fortress
Fract to break fracture, fraction
Ject Throw projection, rejection
Jud Judge judicial, prejudice
Mal Bad malevolent, malefactor
Mater Mother material, maternity
Mit to send transmit, admit
Mort Death mortal, mortician

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Multi Many multimedia, multiple
Pater Father paternal, paternity
Port to carry portable, transportation
Rupt to break bankrupt, disruption
scrib/scribe to write inscription, prescribe
sect/sec to cut bisect, section
Sent to feel; to send consent, resent
Spect to look inspection, spectator
Struct to build destruction, restructure
vid/vis to see video, televise
Voc voice; to call vocalize, advocate

Common Greek Roots

Greek
Definition Examples
Root
Anthropo man; human; humanity anthropologist, philanthropy
Auto Self autobiography, automobile
Bio Life biology, biography
Chron Time chronological, chronic
Dyna Power dynamic, dynamite
Dys bad; hard; unlucky dysfunctional, dyslexic
Gram thing written epigram, telegram
Graph Writing graphic, phonograph
Hetero Different heteronym, heterogeneous
Homo Same homonym, homogenous
Hydr Water hydration, dehydrate
Hypo below; beneath hypothermia, hypothetical
Logy study of biology, psychology
meter/metr Measure thermometer, perimeter
Micro Small microbe, microscope
mis/miso Hate misanthrope, misogyny
Mono One monologue, monotonous
Morph form; shape morphology, morphing

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Nym Name antonym, synonym
Phil Love philanthropist, philosophy
Phobia Fear claustrophobia, phobic
Phon Sound phone, symphony
photo/phos Light photograph, phosphorous
Pseudo False pseudonym, pseudoscience
Psycho soul; spirit psychology, psychic
Scope viewing instrument microscope, telescope
Techno art; science; skill technique, technological
Tele far off television, telephone
Therm Heat thermal, thermometer

Affixes
One method of understanding the meanings of new words is to analyze the
different parts of the word and the meanings of those parts. Many new words
are formed by adding an affixto the beginning or end of a Latin or Greek root or
root word. When affixes are added to the beginning of roots or root words, they
are called prefixes For example, the most common prefix is un-, which
meant not or opposite of. If you add un- to the word happy, the new word
becomes unhappy, which means not happy.

When affixes are added to the end of roots or root words, they are
called suffixes. The most common suffixes are -s and -es, which mean more
than one (or the plural) of the word. Adding -es to wish, changes the meaning o
the word to more than one wish.

Common Prefixes
Prefix Definition Examples
anti- Against anticlimax
de- Opposite devalue
dis- not; opposite of discover
en-, em- cause to enact, empower
fore- before; front of foreshadow, forearm
in-, im- In income, impulse

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in-, im-, indirect, immoral, illiterate,
Not
il-, ir- irreverent
inter- between; among interrupt
mid- Middle midfield
mis- Wrongly misspell
non- Not nonviolent
over- over; too much overeat
pre- Before preview
re- Again rewrite
semi- half; partly; not fully semifinal
sub- Under subway
super- above; beyond superhuman
trans- Across transmit
un- not; opposite of unusual
under- under; too little underestimate

Suffixes

Common Suffixes
Suffix Definition Examples
-able
is; can be affordable, sensible
-ible
-al, -ial having characteristics of universal, facial
-er More taller
-est the most tallest
-ful full of helpful
-ic having characteristics of poetic
-ion submission, motion,
act; process
-tion relation, edition
-ity
state of activity, society
-ty
-less Without hopeless

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-ly how something is lovely
-ment state of being; act of contentment
-ness state of; condition of openness
-ous riotous, courageous,
-eous having qualities of
gracious
-ious
-y characterized by gloomy

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 Commonly Confused ▪ altar - sacred platform or
Words place
alter - to change
A

▪ altogether - thoroughly
▪ accept - to receive
all together – everyone or
except - with the exclusion
everything in one place
of

▪ a lot - a quantity; many of

▪ advice - recommendation
something
(noun)
allot - to divide or portion
advise - to recommend (verb)
out

▪ adverse - unfavorable
▪ angel - supernatural being,
averse - opposed to
good person
angle - shape made by
▪ affect - to influence (verb);
joining 2 straight lines
emotional response (noun)
effect - result (noun); to
▪ are - plural form of "to be"
cause (verb)
our - plural form of "my"

▪ aisle - space between rows

▪ accent - pronunciation
isle - island
common to a region
ascent - the act of rising or
▪ allude - to make indirect
climbing
reference to
assent - consent, agreement
elude - to avoid

▪ assistance - help
▪ allusion - indirect reference
assistants – helpers
illusion - false idea,
misleading appearance
B
▪ bare - nude, unadorned
▪ already - by this time
bear - to carry; an animal
all ready - fully prepared

26 | S t e p U p L e a r n i n g S o l u t i o n s
▪ beside - close to; next to chose - past tense of "to
besides - except for; in choose"
addition ▪ clothes - garments
cloths - pieces of fabric
▪ boar - a wild male pig
bore - to drill a hole through ▪ coarse - rough
course - path; series of
▪ board - piece of wood lectures
bored - uninterested
▪ complement - something
▪ born - brought into life that completes
borne - past participle of "to compliment - praise, flattery
bear" (carry)
▪ conscience - sense of
▪ breath - air taken in (noun) morality
breathe - to take in air (verb) conscious - awake, aware

▪ brake - device for stopping ▪ corps - regulated group

break - destroy; make into corpse - dead body
pieces
▪ council - governing body
▪ buy - to purchase counsel - advice; to give
by - next to; through the advice
agency of
D
C
▪ dairy - place where milk
▪ canvas - heavy cloth products are processed
canvass - to take a survey; a diary - personal journal
survey
▪ descent - downward
▪ capital - major city movement
capitol - government building dissent - disagreement

▪ choose - to pick

27 | S t e p U p L e a r n i n g S o l u t i o n s
▪ dessert - final, sweet course ▪ elicit - to draw out
in a meal illicit - illegal, forbidden
desert - to abandon; dry,
sandy area ▪ eminent - prominent
imminent - about to happen
▪ device - a plan; a tool or
utensil ▪ envelop - to surround (verb)
devise - to create envelope - container for a
letter (noun)
▪ discreet - modest, prudent
behavior ▪ everyday - routine,
discrete - a separate thing, commonplace, ordinary (adj.)
distinct every day - each day,
succession (adj. + noun)
▪ do - a verb indicating
performance or execution of a F
task
dew - water droplets ▪ fair - light skinned; just,
condensed from air honest; a carnival
due - as a result of fare - money for
transportation; food
▪ dominant -commanding,
controlling ▪ farther - at a
dominate - to control greater(measurable) distance
further - in greater(non-
▪ die - to lose life; one of a pair measurable) depth
of dice
dye - to change or add color ▪ formally - conventionally,
with ceremony
▪ dyeing - changing or adding formerly - previously
color
▪ dying - losing life ▪ forth - forward
fourth - number four in a list
E
G

28 | S t e p U p L e a r n i n g S o l u t i o n s
▪ gorilla - animal in ape family ▪ know - to comprehend
guerrilla - soldier specializing no – negative
in surprise attacks
H L

▪ hear - to sense sound by ear ▪ later - after a time

here - in this place latter - second one of two
things
▪ heard - past tense of "to
hear" ▪ lead - heavy metal substance;
herd - group of animals to guide
led - past tense of "to lead"
▪ hoard - a hidden fund or
supply, a cache ▪ lessen - to decrease
horde - a large group or lesson - something learned
crowd, swarm and/or taught

▪ hole - opening ▪ lightning - storm-related

whole - complete; an entire electricity
thing lightening - making lighter

▪ human - relating to the ▪ loose - unbound, not tightly

species homo sapiens fastened
humane – compassionate lose - to misplace

I M

▪ its - possessive form of "it" ▪ maybe - perhaps (adv.)

it's - contraction for "it is" may be - might be (verb)

K ▪ meat - animal flesh

meet - to encounter
▪ knew - past tense of "know" mete - to measure; to
new - fresh, not yet old distribute

29 | S t e p U p L e a r n i n g S o l u t i o n s
 peek - to peer through or look
▪ metal - a hard organic furtively
substance pique - fit of resentment,
medal - a flat disk stamped feeling of wounded vanity
with a design
mettle - courage, spirit, ▪ pedal - the foot lever of a
energy bicycle or car
petal - a flower segment
▪ miner - a worker in a mine peddle - to sell
minor - underage person
(noun); less important (adj.) ▪ personal - intimate; owned
by a person
▪ moral - distinguishing right personnel - employees
from wrong; lesson of a fable
or story ▪ plain - simple, unadorned
morale - attitude or outlook plane - to shave wood;
usually of a group aircraft (noun)

P ▪ precede - to come before

proceed - to continue
▪ passed - past tense of "to
pass" ▪ presence - attendance; being
▪ past - at a previous time at hand
presents - gifts
▪ patience - putting up with
annoyances ▪ principal - foremost (adj.);
patients - people under administrator of a school
medical care (noun)
principle - moral conviction,
▪ peace - absence of war basic truth
piece - part of a whole;
musical arrangement Q

▪ peak - point, pinnacle, ▪ quiet - silent, calm

maximum quite - very

30 | S t e p U p L e a r n i n g S o l u t i o n s
 ▪ scene - place of an action;
R segment of a play
seen - viewed; past participle
▪ rain - water drops falling; to of "to see"
fall like rain
reign - to rule ▪ sense - perception,
rein - strap to control an understanding
animal (noun); to guide or since - measurement of past
control (verb) time; because

▪ raise - to lift up ▪ sight - scene, view, picture

▪ raze - to tear down site - place, location
cite - to document or quote
▪ rational - having reason or (verb)
understanding
▪ rationale - principles of ▪ stationary - standing still
opinion, beliefs stationery - writing paper

▪ respectfully - with respect ▪ straight - unbending

▪ respectively - in that order strait - narrow or confining; a
waterway
▪ reverend - title given to
clergy; deserving respect T
reverent - worshipful
▪ taught - past tense of "to
▪ right - correct; opposite of teach"
left taut - tight
rite - ritual or ceremony
write - to put words on paper ▪ than - besides
then - at that time; next
▪ road - path
rode - past tense of "to ride" ▪ their - possessive form of
"they"
S there - in that place

31 | S t e p U p L e a r n i n g S o l u t i o n s
 they're - contraction for "they ▪ where - in which place
are" were - past tense of "to be"

▪ through - finished; into and ▪ which - one of a group

out of witch - female sorcerer
threw - past tense of "to
throw" ▪ whose - possessive for "of
thorough - complete who"
who's -contraction for "who
▪ to - toward is"
too - also; very (used to show
emphasis) Y
two - number following one
▪ your - possessive for "of you"
▪ track - course, road you're - contraction for "you
tract - pamphlet; plot of are"
ground yore - time long past

▪ waist - midsection of the

body
waste - discarded material;
to squander
▪ waive - forgo, renounce
wave - flutter, move back and
forth

▪ weak - not strong

▪ week - seven days

▪ weather - climatic condition

whether - if
wither – shrivel

32 | S t e p U p L e a r n i n g S o l u t i o n s
 Idioms Ball is in your court - It is up to
you to make the next decision or
step
Idioms are groups of words that can
mean things other than what they Barking up the wrong tree -
say. The meanings vary from Looking in the wrong place. Accusing
location to location and possibly the wrong person
speaker to speaker, and they often
depend on context for meaning. Be glad to see the back of -Be
happy when a person leaves.
A hot potato - Speak of an issue
Beat around the bush -Avoiding
which many people are talking about
and which is usually disputed the main topic. Not speaking directly
about the issue.
A penny for your thoughts - A
Best of both worlds -All the
way of asking what someone is
advantages.
thinking

Actions speak louder than words Best thing since sliced bread -A
good invention or innovation. A good
- People's intentions can be judged
better by what they do than what idea or plan.

they say. Bite off more than you can chew

-To take on a task that is way too
Add insult to injury - To further a
loss with mockery or indignity; to big.

worsen an unfavorable situation. Blessing in disguise - Something

An arm and a leg - Very expensive good that isn't recognized at first.

or costly. A large amount of money. Burn the midnight oil - To work

At the drop of a hat - Meaning: late into the night, alluding to the

without any hesitation; instantly. time before electric lighting.

Can't judge a book by its cover -

Back to the drawing board -When
an attempt fails and it's time to start Cannot judge something primarily on
appearance.
all over.

Caught between a rock and a

hard place - When someone finds

33 | S t e p U p L e a r n i n g S o l u t i o n s
it difficult to choose between two Don't put all your eggs in one
alternatives. basket - Do not put all your
resources in one possibility.
Costs an arm and a leg -This idiom
is used when something is very Drastic times call for drastic
expensive. measures - When you are
extremely desperate you need to
Cross that bridge when you come
take drastic actions.
to it -Deal with a problem if and
when it becomes necessary, not Elvis has left the building - The
before. show has come to an end. It's all
over.
Cry over spilt milk -When you
complain about a loss from the past. Every cloud has a silver lining -
Be optimistic, even difficult times will
Curiosity killed the cat -Being
lead to better days.
Inquisitive can lead you into an
unpleasant situation. Far cry from - Very different from.

Cut corners - When something is Feel a bit under the weather -

done badly to save money. Meaning: Feeling slightly ill.

Cut the mustard - To succeed; to Give the benefit of the doubt -

come up to expectations; adequate Believe someone's statement,
enough to compete or participate without proof.

Devil's Advocate - To present a Hear it on the grapevine - This

counter argument idiom means 'to hear rumors' about
something or someone.
Don't count your chickens before
the eggs have hatched - This Hit the nail on the head - Do or
idiom is used to express "Don't make say something exactly right
plans for something that might not
Hit the sack / sheets / hay - To
happen".
go to bed.
Don't give up the day job -You are
In the heat of the moment -
not very good at something. You
Overwhelmed by what is happening
could definitely not do it
in the moment.
professionally.

34 | S t e p U p L e a r n i n g S o l u t i o n s
It takes two to tango - Actions or Not playing with a full deck -
communications need more than one Someone who lacks intelligence.
person
Off one's rocker -Crazy, demented,
Jump on the bandwagon -Join a out of one's mind, in a confused or
popular trend or activity. befuddled state of mind, senile.

Keep something at bay - Keep On the ball - When someone

something away understands the situation well.

Kill two birds with one stone - Once in a blue moon -Happens
This idiom means, to accomplish two very rarely.
different things at the same time.
Picture paints a thousand words
Last straw - The final problem in a -A visual presentation is far more
series of problems. descriptive than words.

Let sleeping dogs lie -Do not Piece of cake -A job, task or other
disturb a situation as it is - since it activity that is easy or simple.
would result in trouble or
Put wool over other people's
complications.
eyes - This means to deceive
Let the cat out of the bag - To someone into thinking well of them.
share information that was
See eye to eye -This idiom is used
previously concealed
to say that two (or more people)
Make a long story short - Come to agree on something.
the point - leave out details
Sit on the fence - This is used
Method to my madness - An when someone does not want to
assertion that, despite one's choose or make a decision.
approach seeming random, there
Speak of the devil -This expression
actually is structure to it.
is used when the person you have
Miss the boat - This idiom is used just been talking about arrives.
to say that someone missed his or
Steal someone's thunder -To take
her chance
the credit for something someone
Not a spark of decency - No else did.
manners

35 | S t e p U p L e a r n i n g S o l u t i o n s
Take with a grain of salt -This
means not to take what someone
says too seriously.

Taste of your own medicine -

Means that something happens to
you, or is done to you, that you have
done to someone else

To hear something straight from

the horse's mouth -To hear
something from the authoritative
source.

Whole nine yards -Everything. All

of it.

Wouldn't be caught dead -Would

never like to do something

Your guess is as good as mine -

To have no idea, do not know the
answer to a question

36 | S t e p U p L e a r n i n g S o l u t i o n s
Subject Verb Agreement

A singular subject agrees with a singular verb, and a plural subject agrees with a
plural verb. A singular subject involves a single item or person: “the book” or “a
surgical patient.” A plural subject involves more than one item or person: “some
badly written hospital signs” or “the shocked copy editors.”

Rules

1. When the subject of a sentence is composed of two or more nouns or

pronouns connected by and, use a plural verb.

She and her friends are at the fair.

2. When two or more singular nouns or pronouns are connected by or or

nor, use a singular verb.

The book or the pen is in the drawer.

3. When a compound subject contains both a singular and a plural noun

or pronoun joined by or or nor, the verb should agree with the part of
the subject that is nearer the verb.

Either the boy or his friends were punished.

Either his friends or the boy was punished.

This also applies to not only. . .but also, and neither. . .nor. The subject
closest to the verb determines whether the verb is singular or plural.

Neither the teacher nor the students write on the blackboard.

4. The words each, each one, either, neither, everyone, everybody,

anybody, anyone, nobody, somebody, someone, and no one are singular
and require a singular verb.

Each of these hot dogs is juicy.

Nobody is here.

Everybody helps when there is a crisis.

Somebody wants to speak to you.

Either is correct.

37 | S t e p U p L e a r n i n g S o l u t i o n s
5. Expressions such as with, together with, including, accompanied by,
in addition to, or as well do not change the number of the subject. If the
subject is singular, the verb is too.

The President, accompanied by his wife, is traveling to India.

All of the books, including yours, are in that box.

6. Measurements of money, time, and distance usually require a singular

verb.4

One hundred dollars is a lot of money for a bottle of wine.

Two hours is a long time to wait to see a doctor.

93,000,000 miles is the distance from the sun to the earth.

7. The following words almost always use the plural form of verbs: all,
both,few, many, several, and some.

Some people in my office are very annoying

Few mountain climbers have successfully reached the peak of Mt. Everest.

8. The word none needs special attention. Sometimes it uses a singular

verb, and at other times, it uses a plural verb. When none means no one
or not one, use the singular form of the verb. When none means or
suggests more than one thing or person, use the plural form of the verb.

None of them is able to do that job.

None are helpless because they can always try.

9. In sentences beginning with "there is" or "there are," or “here is”, or

“here are” the subject follows the verb. The verb agrees with what
follows.

There are many questions.

There is a question.

Here is my jacket.

Here are my shoes

38 | S t e p U p L e a r n i n g S o l u t i o n s
10. When the word number is preceded with the word a, use a plural
verb. When the word number is preceded with the word the, use a
singular verb.

A number of people are waiting to see you.

The number of stars in the sky seems countless.

11. Nouns such as scissors, tweezers, trousers, and shears require

plural verbs. (There are two parts to these things.)

These scissors are dull.

Those trousers are made of wool.

12. Collective nouns are words that imply more than one person but that
are considered singular and take a singular verb, such as group, team,
committee, class, and family.

The team runs during practice.

The committee decides how to proceed.

My family has never been able to agree.

The crew is preparing to dock the ship.

The jury has reached a verdict.

39 | S t e p U p L e a r n i n g S o l u t i o n s
Exercise

Choose the correct form of the verb that agrees with the subject.

1. Annie and her brothers (is, are) at school.

2. Either my mother or my father (is, are) coming to the meeting.

3. The dog or the cats (is, are) outside.

4. Either my shoes or your coat (is, are) always on the floor.

5. George and Tamara (doesn't, don't) want to see that movie.

6. Benito (doesn't, don't) know the answer.

7. One of my sisters (is, are) going on a trip to France.

8. The man with all the birds (live, lives) on my street.

9. The movie, including all the previews, (take, takes) about two hours to watch.

10. The players, as well as the captain, (want, wants) to win.

11. Either answer (is, are) acceptable.

12. Every one of those books (is, are) fiction.

13. Nobody (know, knows) the trouble I've seen.

14. (Is, Are) the news on at five or six?

15. Mathematics (is, are) John's favorite subject, while Civics (is, are) Andrea's
favorite subject.

16. Eight dollars (is, are) the price of a movie these days.

17. (Is, Are) the tweezers in this drawer?

18. Your pants (is, are) at the cleaner's.

40 | S t e p U p L e a r n i n g S o l u t i o n s
19. There (was, were) fifteen candies in that bag. Now there (is, are) only one
left!

20. The committee (debates, debate) these questions carefully.

41 | S t e p U p L e a r n i n g S o l u t i o n s
Exercise - Parallel Structure

Mark the correct sentence.

1. A____ Jennifer is smart, beautiful, and loves everyone.

B____ Jennifer is smart, beautiful, and caring.

2. A____ Andy’s day is so long that he gets up at 6:00 a.m., leaves for work at
6:30 a.m., is eating dinner at 11:00 p.m., and goes to bed at 2:00 a.m.
B____ Andy’s day is so long that he gets up at 6:00 a.m., leaves for work at
6:30 a.m., eats dinner at 11:00 p.m., and goes to bed at 2:00 a.m.

3. A____ Bob was not only Sam’s roommate, but also he was his best friend.
B____ Bob was not only Sam’s roommate but also his best friend.

4. A____ If you go to the store, please remember to pick up your prescription,

buy some shampoo, and to look for a notebook.
B____ If you go to the store, please remember to pick up your prescription, to
buy some shampoo, and to look for a notebook.

5. A____ I spent two hours with Ms. Smith, reviewing my job performance,
evaluating my goals, and discussing my future with the company.
B____ I spent two hours with Ms. Smith, reviewing my job performance,
evaluating my goals, and my future with the company was also discussed.

6. A_____ Mr. Brown’s lecture was inaccurate, boring, and unnecessary.

B_____ Mr. Brown’s lecture was inaccurate, boring, and should have been
omitted.

7. A_____ Most people play golf for pleasure, for exercise, and for social
contacts.
B_____ Most people play golf for pleasure, for exercise, and so they can meet
people.

42 | S t e p U p L e a r n i n g S o l u t i o n s
8. A____ The most dangerous forms of transportation are bicycles, cars, and
riding a motorcycle. B____ The most dangerous forms of transportation are
bicycles, cars, and motorcycles.

9. A____ Many people share the same three fears: making speeches, being in
high places, and numbers.
B____ Many people share the same three fears: making speeches, being in high
places, and working with numbers.

10. A____ At the body shop, the car was sanded to the bare metal, painted
with primer, and sprayed with blue enamel.
B____ At the body shop, the car was sanded to the bare metal, painted with
primer, and blue enamel was sprayed on.

43 | S t e p U p L e a r n i n g S o l u t i o n s
Punctuation

Punctuation is used to create sense, clarity and stress in sentences. You use
punctuation marks to structure and organize your writing.

A. The Period

The period (known as a full stop in British English) is probably the simplest of
the punctuation marks to use. It is used to break up sentences at the end of a
logical and complete thought. It can also be used to indicate an abbreviation.

I was born in Australia and now live in Indonesia.

The Dalai Lama is the spiritual leader of the Tibetan people.

I will arrive between 6 a.m. and 7 a.m.

We are coming on Fri., Jan. 4.

B. The Apostrophe

The apostrophe has three uses:

1. To form possessives of nouns

2. To show the omission of letters
3. To indicate certain plurals of lowercase letters

Forming Possessives of Nouns

add 's to the singular form of the word (even if it ends in -s):

the owner's car

James's hat

add 's to the plural forms that do not end in -s:

the children's game

44 | S t e p U p L e a r n i n g S o l u t i o n s
 the geese's honking

add ' to the end of plural nouns that end in -s:

two cats' toys

three friends' letters

the countries' laws

add 's to the end of compound words:

my brother-in-law's money

add 's to the last noun to show joint possession of an object:

Todd and Anne's apartment

Showing omission of letters

Apostrophes are used in contractions. A contraction is a word (or set of

numbers) in which one or more letters (or numbers) have been omitted. The
apostrophe shows this omission. Contractions are common in speaking and in
informal writing. To use an apostrophe to create a contraction, place an
apostrophe where the omitted letter(s) would go.

don't = do not

I'm = I am

he'll = he will

who's = who is

shouldn't = should not

didn't = did not

Forming plurals of lowercase letters

45 | S t e p U p L e a r n i n g S o l u t i o n s
Apostrophes are used to form plurals of letters that appear in lowercase. To form
the plural of a lowercase letter, place 's after the letter.:

Dave's mother constantly stressed minding one's p's and q's.

C. Parentheses

Parentheses can be used to show elements in a sentence that are related, yet
not necessary to understand the meaning of the sentence. Parentheses can be
replaced by commas in most cases, although the use of parentheses tends to
de-emphasize a particular piece of information.

My family visited several countries (Italy, France, and Spain) on our vacation
last year.

D. Commas

1. Use commas to separate independent clauses when they are joined by any of
these seven coordinating conjunctions: and, but, for, or, nor, so, yet.

▪ I met Henry, we went for a swim together, and afterwards Harry went
home.

2. Use commas after introductory a) clauses, b) phrases, or c) words that come

before the main clause.

▪ Hearing that her father was in hospital, Jane left work immediately.
▪ Walking to the bus stop that morning, Sam knew it was going to be a
special day.

3. Use a pair of commas in the middle of a sentence to set off clauses, phrases,
and words that are not essential to the meaning of the sentence. Use one
comma before to indicate the beginning of the pause and one at the end to
indicate the end of the pause.

▪ China, one of the most powerful nations on Earth, has a huge population.
▪ Jason's grandmother, who was born in 1930, lived through the Second
World War.

46 | S t e p U p L e a r n i n g S o l u t i o n s
 ▪ Cats, unlike dogs, do not respect their masters.
▪ My friend, Jim, likes to go scuba diving.

4. Use commas to separate three or more words, phrases, or clauses written in a

series.

▪ The car smashed into the wall, flipped onto its roof, slid along the road,
and finally stopped against a tree.
▪ The dog leapt into the air, snatched the frisbee in its mouth, landed, and
ran off into the forest.

5. Use commas to separate two or more coordinate adjectives that describe the
same noun. Be sure never to add an extra comma between the final adjective
and the noun itself or to use commas with non-coordinate adjectives.

▪ She was young, beautiful, kind, and intelligent.

▪ The house we visited was dark, dreary, and run-down.

6. Use commas to set off all geographical names, items in dates (except the
month and day), addresses (except the street number and name), and titles in
names.

7. Use a comma to shift between the main discourse and a quotation.

E. Hyphen

Two words brought together as a compound may be written separately, written

as one word, or connected by hyphens.

1. Use a hyphen to join two or more words serving as a single adjective

before a noun:

a one-way street
chocolate-covered peanuts
well-known author

However, when compound modifiers come after a noun, they are not
hyphenated:

47 | S t e p U p L e a r n i n g S o l u t i o n s
 The peanuts were chocolate covered.
The author was well known.

2. Use a hyphen to avoid confusion or an awkward combination of letters:

re-sign a petition (vs. resign from a job)

3. Use a hyphen with the prefixes ex- (meaning former), self, mid; with the
suffix -elect; between a prefix and a capitalized word; and with figures or
letters:

ex-husband
self-assured
mid-September
mayor-elect
anti-American
pre-Civil War
mid-1980s

4. Use a hyphen to divide words at the end of a line if necessary, and make
the break only between syllables:

pref-er-ence
sell-ing
in-di-vid-u-al-ist

F. Quotation Marks

The primary function of quotation marks is to set off and represent exact
language (either spoken or written) that has come from somebody else.

Direct quotations involve incorporating another person's exact words into your
own writing.

1. Quotation marks always come in pairs. Do not open a quotation and fail to
close it at the end of the quoted material.

48 | S t e p U p L e a r n i n g S o l u t i o n s
2. Capitalize the first letter of a direct quote when the quoted material is a
complete sentence.

Mr. Johnson, who was working in his field that morning, said, "The alien
spaceship appeared right before my own two eyes."

49 | S t e p U p L e a r n i n g S o l u t i o n s
Exercise: Punctuation

Put appropriate punctuation marks in the following sentences.

1. The men in question Harold Keene, Jim Peterson, and Gerald Greene deserve
awards.
________________________________________________________________
________________________________________________________________
____________________________

2. Several countries participated in the airlift Italy, Belgium, France, and

Luxembourg.
________________________________________________________________
________________________________________________________________
____________________________

3. Only one course was open to us surrender, said the ex-major, and we did.
________________________________________________________________
________________________________________________________________
____________________________

4. Judge Carswell later to be nominated for the Supreme Court had ruled against
civil rights.
________________________________________________________________
________________________________________________________________
____________________________

5. In last week's New Yorker, one of my favorite magazines, I enjoyed reading

Leland's article How Not to Go Camping.
________________________________________________________________
________________________________________________________________
____________________________

6. Yes, Jim said, I'll be home by ten.

50 | S t e p U p L e a r n i n g S o l u t i o n s
________________________________________________________________
________________________________________________________________
____________________________

7. There was only one thing to do study till dawn.

________________________________________________________________
________________________________________________________________
____________________________

8. Montaigne wrote the following A wise man never loses anything, if he has
himself.
________________________________________________________________
________________________________________________________________
____________________________

9. The following are the primary colors red, blue, and yellow.
________________________________________________________________
________________________________________________________________
____________________________
________________________________________________________________
________________________________________________________________
____________________________

10. Arriving on the 8 10 plane were Liz Brooks, my old roommate her husband
and Tim, their son.
________________________________________________________________
________________________________________________________________
____________________________

11. When the teacher commented that her spelling was poor, Lynn replied All
the members of my family are poor spellers. Why not me?
________________________________________________________________
________________________________________________________________
____________________________

12. He used the phrase you know so often that I finally said No, I don't know.

51 | S t e p U p L e a r n i n g S o l u t i o n s
________________________________________________________________
________________________________________________________________
____________________________

13. The automobile dealer handled three makes of cars Volkswagens, Porsches,
and Mercedes Benz.
________________________________________________________________
________________________________________________________________
____________________________

14. Though Phil said he would arrive on the 9 19 flight, he came instead on the
10 36 flight.
________________________________________________________________
________________________________________________________________
____________________________

15. Whoever thought said Helen that Jack would be elected class president?
________________________________________________________________
________________________________________________________________
____________________________

52 | S t e p U p L e a r n i n g S o l u t i o n s
Active / Passive Verb Forms

Sentences can be active or passive. Therefore, tenses also have "active forms"
and "passive forms."

Active Form

In active sentences, the agent of the action is the subject of the sentence and
the receiver of the action is the object.

[agent of the action] + [verb] + [receiver of the action]

Examples:

Mike washes the dishes

agent of the action Verb receiver of the action

Passive Form

In passive sentences, the receiver of the action is the subject of the sentence
and the agent of the action is optionally included near the end of the sentence.
You can use the passive form if you think that the thing receiving the action is
more important or should be emphasized. You can also use the passive form if
you do not know who is doing the action or if you do not want to mention who is
doing the action.

[Receiver of the action] + [be] + [past participle of verb] + [by] + [agent of the
action]

Examples:

The dishes are washed by Mike

Subject receiving the Passive verb agent of the action
action

53 | S t e p U p L e a r n i n g S o l u t i o n s
Overview

Tense Active Passive

Simple Once a month, Kate cleans the Once a month, the attic is
Present attic. cleaned by Kate.

Present Right now, Mike is writing the Right now, the report is being
Continuous report. written by Mike.

Oliver repaired the bike. The bike was repaired by

Simple Past
Oliver.

The salesman was The client was being

Past
advising the client when the advised by the salesman when
Continuous
thief came into the store. the thief came into the store.

Present Many tourists have That fort has been visited by

Perfect visited that fort. many tourists.

Present Recently, Sarah has been Recently, the work has been
Perfect doing the work. being done by Sarah.
Continuous

David had repaired many Many vehicles had been

Past Perfect vehicles before he received his repaired by David before he
mechanic's license. received his mechanic's license.

Chef Brown had been The restaurant's fantastic

preparing the restaurant's dinners had been being
Past Perfect
fantastic dinners for two years prepared by Chef Brown for
Continuous
before he moved to Spain. two years before he moved to
Spain.

Simple Someone will finish the The analysis will be

Future analysis by 7:00 PM. finished by 7:00 PM.
will

54 | S t e p U p L e a r n i n g S o l u t i o n s
Simple Lauren is going to Dinner is going to be
Future make dinner tonight. made by Lauren tonight.
be going to

Future At 8:00 PM tonight, Dave will At 8:00 PM tonight, the

Continuous be washing the dishes. dishes will be being
will washed by Dave.

Future At 8:00 PM tonight, Dave is At 8:00 PM tonight, the

Continuous going to be washing the dishes are going to be being
be going to dishes. washed by Dave.

Future They will have completed the The report will have been
Perfect report before the deadline. completed before the
will deadline.

Future They are going to have The report is going to have

Perfect completed the report before been completed before the
be going to the deadline. deadline.

Future The famous artist will have The mural will have been
Perfect been painting the mural for being painted by the famous
Continuous over six months by the time it artist for over six months by
will is finished. the time it is finished.

The famous artist is going to The mural is going to have

Future
have been painting the mural been being painted by the
Perfect
for over six months by the time famous artist for over six
Continuous
it is finished. months by the time it is
be going to
finished.

55 | S t e p U p L e a r n i n g S o l u t i o n s
Exercise- Active and Passive Voice

Rewrite the following sentences so that the verbs will be in the active
voice.

1. We are taught grammar by Ms Sullivan.

________________________________________________________________
________________________________________________________________
____________________________

2. He was praised by the teacher.

________________________________________________________________
________________________________________________________________
____________________________

3. The injured were taken to the hospital by the firemen.

________________________________________________________________
________________________________________________________________
____________________________

4. The town was destroyed by an earthquake.

________________________________________________________________
________________________________________________________________
____________________________

5. The teacher was pleased with the boy’s work.

________________________________________________________________
________________________________________________________________
____________________________

6. The building was damaged by the fire.

________________________________________________________________
________________________________________________________________
____________________________

56 | S t e p U p L e a r n i n g S o l u t i o n s
7. By whom were you taught French?
________________________________________________________________
________________________________________________________________
____________________________

8. You will be given a ticket by the manager.

________________________________________________________________
________________________________________________________________
____________________________

9. The streets were thronged with spectators.

________________________________________________________________
________________________________________________________________
____________________________

10. We will be blamed by everyone.

________________________________________________________________
________________________________________________________________
____________________________

11. The trees were blown down by the wind.

________________________________________________________________
________________________________________________________________
____________________________

12. The thieves were caught by the police.

________________________________________________________________
________________________________________________________________
____________________________

13. The letter was posted by Alice.

________________________________________________________________
________________________________________________________________
____________________________

57 | S t e p U p L e a r n i n g S o l u t i o n s
14. We were received by the hostess.
________________________________________________________________
________________________________________________________________
____________________________

15. The snake was killed with a stick.

________________________________________________________________
________________________________________________________________
____________________________

58 | S t e p U p L e a r n i n g S o l u t i o n s
Logical Reasoning & Data
Interpretation

59 | S t e p U p L e a r n i n g S o l u t i o n s
Statement & Courses of Action

Evaluating courses of action is a Major area of logical reasoning. This type of questions is
intended to scrutinize the decision -making skills of the candidate. A small case
study highlighting either a problem or an area that can be improved is
presented. This is followed by different courses of action. The candidate is
required to study the situation and choose the option that will solve the problem
or improve the situation.

Question Structure

Directions: - In the following questions a fact situation is given followed by two

suggested courses of action. A course of action is a step of administrative
decision taken for improvement or follow- up action. Read the situation and then
decide which of the given courses of action follows.

Choose the option,

1) If only course of action I follows

2) If only course of action II follows
3) If both the course of action follow
4) If neither follows
5) If the data given is inadequate i.e., if in the light of the given information. It
cannot be asserted with certainty whether a course of action follows or not.

Eg: Statement: Cholera has affected many parts of the country.

Courses of Action:
I. The MLAs should rush to their constituencies.
II. The government should try to make people aware about the need for
clean drinking water.

Steps to evaluate a Course Of Action

We can classify the question into two patterns or types.

A. The first pattern talks of a problem and the suggested courses of action talk
of a solution.

60 | S t e p U p L e a r n i n g S o l u t i o n s
B. The second pattern talks of a situation or fact and the courses of actions or
ways of improving that situation.

A. Problem Solution Relation

In this type of pattern, the suggested course of action can be followed if.

▪ It solves / reduces or minimizes the problem. A suggested course of

actions can be said to solve/reduce/minimize, the problem. When it is an
established fact. ie, It is acknowledged universally as a fact. It is an
established fact that accidents can be minimized if the motorists follow
traffic rules.
Example
Main Statement: Accidents are increasing in the state of Kerala.
Valid Course of Action: An awareness campaign conducted to make people
aware of the importance of traffic rules.

▪ the solution or course of action is practically possible. A suggested course

of action may indeed solve a problem but in practical life it may not be
advisable or possible. If it is so, then the course of action is rejected.
Example
Statement: Accidents are increasing in our state.
Course of action: The production of vehicles should be banned.
Though the above course of action minimizes the problem, it is practically
impossible.

B. Situation - Improvement Relation

This pattern is solved just by applying the same rules of Type I. First we have to
identify whether the fact or situation will improve due to the course of action
mentioned. Second thing to do is to check whether the, course of action is
practically possible.

Note

Never allow our personal perceptions to come into play while evaluating the
suggested courses of action. Our decisions and views should be impartial and
impersonal.

61 | S t e p U p L e a r n i n g S o l u t i o n s
Syllogism

Key Concepts

I. Some A is B.

The Diagram for Some A is B is

The possible conclusions are,

1) Some A is B

2) Some B is A

II - Some A is B and Some B is C

The Diagram is,

Now the Possible Conclusions are,

62 | S t e p U p L e a r n i n g S o l u t i o n s
Between A and B Between B and C

Some A is B Some B is C

Some B is A Some C is B

There is no direct connection between A and C. So it is not possible to derive any

conclusion between A and C.

III. All A is B

The Diagram is,

The Conclusions are,

All A is B.

Some A is B.

Some B is A.

Note : When the statements are positive, the conclusions must be positive.

IV – All A is B and All B is C

63 | S t e p U p L e a r n i n g S o l u t i o n s
The Conclusions are,

Between A and B Between B and C Between A and

C

All A is B. All B is C. All A is C.

Some A is B. Some B is C. Some A is C.

Some B is A. Some C is B. Some C is A.

V - Some A is B. All B is C.

The possible conclusions are,

Between A and B Between B and C Between A and C

Some A is B All B is C Some A is C

Some B is A Some B is C Some C is A

Some C is B

64 | S t e p U p L e a r n i n g S o l u t i o n s
VI - All A is B and Some B is C

The possible conclusions are,

Between A and B Between B and C

All A is B Some B is C

Some A is B Some C is B

Some B is A

There is no DIRECT CONNECTION between A and C. So it is not possible to

derive any conclusion between A and C.

VII– All B is A and All C is A

The Possible Conclusions are,

65 | S t e p U p L e a r n i n g S o l u t i o n s
Between A and B Between A and C

All B is A All C is A

Some B is A Some C is A

Some A is B Some A is C

There is no DIRECT CONNECTION between B and C. So it is not possible to

derive any conclusion between B and C.

VIII- No A is B

The Possible Conclusions are,

No A is B

No B is A

Some A is not B

Some B is not A

When NO comes in Statement, Some-not should follow in Conclusion

66 | S t e p U p L e a r n i n g S o l u t i o n s
IX - All A is B and No B is C

The Possible Conclusions are,

Between A and B Between B and C Between A and C

All A is B No B is C No A is C

Some A is B No C is B Some A is Not C

Some B is A Some B is not C

Some C is not B

X – All A is B and No A is C

The Possible Conclusions are,

Between A and B Between A and C Between B and C

All A is B No A is C Some B is not C

Some A is B No C is A

Some B is A Some A is not C

Some C is not A

67 | S t e p U p L e a r n i n g S o l u t i o n s
XI - Some A is B; No B is C

The Possible Conclusions are,

Between A and B Between B and C Between A and C

Some A is B No B is C Some A is not C

Some B is A No C is B

Some B is not C

Some C is not B

XII- Some A is B; No A is C

The Possible Conclusions are,

Between A and B Between A and C Between B and C

Some A is B No A is C Some B is not C

Some A is not C

Some C is not A

68 | S t e p U p L e a r n i n g S o l u t i o n s
 Blood Relations

These questions involve analysis of information showing blood relationship

among members of a family. In these question a chain of relationships is given
in the form of information and you are supposed to find out the relationship
between specified members of the chain.

The below table list the most common relationship types:

Brother Don of Mother/Father

Sister Daughter of Mother/ Father
Uncle Brother of Mother/Father
Aunt Sister of Mother/Father
Nephew Brother’s or Sister’s Son
Niece Brother’s or Sister’s Daughter
Grandfather Father of Mother/Father
Grandmother Mother of Mother/Father
Daughter in law Son’s Wife
Son in law Daughter’s Husband
Father in law Husband’s /Wife’s father
Mother in law Husband’s /Wife’s mother
Sister in law Husband’s /Wife’s sister
Brother’s Wife
Brother in law Husband’s /Wife’s brother
Sister’s Husband

First generation : Grand father, Grand mother

Second generation : Father, Mother, Uncle, Aunt.
Third generation : Self, Sister, Brother, Sister in law, Brother in law
Fourth generation : Son, Daughter, Nephew, Niece.

69 | S t e p U p L e a r n i n g S o l u t i o n s
Types of Questions

1. Mixed Blood Relations -

If there are multiple persons involved in the equation it is helpful to solve these
problem with the help of digrams.

Example

A has 3 children. B is the brother of C and C is the sister of D, E who is the wife
of A is the mother of D. There is only one daughter of the husband of E. what is
the relation between D and B?

Solution: With the chart

Therefore, D is a boy because there is only one daughter of E.

Hence, B is the brother of D.

2. Coded Blood Relations:

In this type, relationships represented by codes and symbols like + , - , / , *.

You have to analyze the required relation based on the given code. In this also
you may need diagrammatic representation of problem to solve it.

Example

If A + B means A is the mother of B; A x B means A is the father of B; A $ B

means A is the brother of B and A @ B means A is the sister of B then which of
the following means P is the son of Q?

(A) Q + R @ P @ N (B) Q + R * P @ N

(C) Q x R $ P @ N (D) Q x R $ P $ N

70 | S t e p U p L e a r n i n g S o l u t i o n s
Solution: (D)

Q x R = Q is the mother of R [-Q, ±R]

R $ P = R is the brother of P [+ R, ±P]

P $ N = P is the brother of N [+ P, ±N]

Therefore P is the son of Q.

71 | S t e p U p L e a r n i n g S o l u t i o n s
 Analogy

An analogy compares the relationship between two things or ideas to highlight

some point of similarity. It is a way to clarify an idea or an unfamiliar concept by
comparing it to something familiar.

Question Stem

You will be given a pair of words that have a certain logical relationship to each
other, and you will have to choose a parallel second pair. Now, from the given
four pairs of words, you need to choose a pair of words that has a similar
relationship as the given pair.

Example

Basil: Herb::
A. Wheel: Car
B. water: Reservoir
C. Oak: Tree
D. Boat: Sail

To finish an analogy, you need to decide what relationship exists between the
first two things or ideas. Then apply that relationship to another pair of words
and see if it is the same.

To get the exact pair with the similar relationship, let us analyze each option in
detail. It is always advisable to find out the exact relationship the words in
question shows. The given pair is ‘Basil : Herb’. BASIL is a type of HERB. “Is a
type of” is the relationship. Hence the next pair should also share the same
relationship.

The first option is “wheel : car”.

• Wheel is a part of a car. The relationship is Part-to-whole. This pair does

not have any similarity with the given pair.

72 | S t e p U p L e a r n i n g S o l u t i o n s
The second option is “water : reservoir”

• A reservoir is a place where you find water. This relationship is also not
parallel to the given pair of words.

The third option is “oak : tree”

• Oak is a typ
• e of tree. This pair of words has the same relationship as the first pair.
Let’s consider the fourth option too.

The fourth option is “boat : sail”

• Boat is a means of transportation used to sail. This is an “object to

function” analogy, and this pair of words does not share the same
relationship as the first pair.

As option C has the same relationship as the given pair, it is the correct option.

Types of Analogies

Type Relationship Example

Is similar in Lucky: forturnate

Synonym meaning to
Is opposite in Lament: rejoice
Antonym meaning to
Part to Whole Is a part of Stanza: pem
Cateogary/Type Is a type/kind of Collage: art
Object to Function Is used to Rule: measure
Performer to Does/performs Chef: cook

73 | S t e p U p L e a r n i n g S o l u t i o n s
Related Action
Is a Tornado:
Cause & Effect cause/indication of destruction
Degree & Intensity Is a small/large Irritate: enrage
Symbol & Is a symbol of Dove: peace
Representation

74 | S t e p U p L e a r n i n g S o l u t i o n s
 Coding & Decoding

The coding and decoding of reasoning test is set up to judge the candidate’s
ability to decipher the rule that codes a word/message and break the code to
decipher the message. In questions, a word is given coded in a particular way
and candidates are asked to code the other given word in the same manner as
the first given word was coded.

There are basically five types of coding and decoding questions that are asked in
the examination.

1. Order based questions

2. Substitution for words

3. Number symbol coding

4. Substitution based coding

5. Deciphering number and symbol codes in a message

Question 1 : VICTORY is coded as YLFWRUB, how can SUCCESS be

coded?

(a)VXEEIVV

(b) VYEEHVV

(c)VXFFHVV

(d)VYEFIVV

Solution - Each letter of the word is, moved three steps forward to obtain the
code.

VXFFHVV

Question 2: If BELIEF is written as afkkdi, how is SELDOM written in

that code?

(a)tfkenp

75 | S t e p U p L e a r n i n g S o l u t i o n s
(b)rfkenn

(c)rfkfnp

(d)rdkcnl

Solution:The first, third and fifth letters of the word are each moved one step
back While the second, fourth and sixth letters are respectively mOved one, two
and I steps forward to obtain the corresponding letters of the code.

rfkfnp

Question 3: in a certain code, TOGETHER is written as RQEGRJCT. In the

same code, PAROLE will be written as.

(a)NCPQJG

(b) RCPQJK
(c) NCQPJG

(d)RCTQNG

Solution - The letters at odd positions are each moved two steps backward and
those at positions are each moved two steps forward to obtain the corresponding
lettc the code.

NCPQJG

Question 4: In a certain language, MADRAS is coded as NBESBT, how is

BOMBAY coded in that code?

(a) CPNCBZ

(b)CPNCBX

(c)DPNCBZ

(d)DPNCBX

Solution - Clearly every letter is increased by 1 as

M +1 N
A +1 B

76 | S t e p U p L e a r n i n g S o l u t i o n s
D +1 E
R +1 S
A +1 B
S +1 T
So after increasing every character in work BOMBAY by 1, we get CPNCBZ

Question 5: In a certain code, TRIPPLE is written as SQHOOKD. How is

DISPOSE written in that code ?
(a) EJTQPTF

(b) EJTQPTG

(c)CHRPNRD

(d)CHRONRD

Solution - Clearly every letter is decreased by 1.

77 | S t e p U p L e a r n i n g S o l u t i o n s
 Data Sufficiency

Data sufficiency questions consist of a question followed by two statements.

Your job is to decide whether the information in the statements (taken singly or
together) is sufficient to answer the question.

These questions require much less calculation than standard problem solving:
evaluate rather than calculate.

Steps to approach data sufficiency questions

▪ Read the question and make deductions from the data

▪ Think about what you need to solve the question
▪ Consider the statements one at a time
▪ Do not actually solve the problem

Question 1: What is the value of x?

I. the square of x is 36

II. x(x-6) = 0

A. I alone sufficient while II alone not sufficient to answer

B. II alone sufficient while I alone not sufficient to answer

C. Either I or II alone sufficient to answer

D. Both I and II are not sufficient to answer

E. Both I and II are necessary to answer

Solution:

From statement 1, x = 6 or -6
From statement 2, x = 0 or 6
The answer is E because when the information from both statements is taken
together x = 6

Question 2: What is the two-digit number?

78 | S t e p U p L e a r n i n g S o l u t i o n s
I. The difference between the two digits is 9.

II.The sum of the digits is equal to the difference between the two digits.

A. I alone sufficient while II alone not sufficient to answer

B. II alone sufficient while I alone not sufficient to answer

C. Either I or II alone sufficient to answer

D. Both I and II are not sufficient to answer

E. Both I and II are necessary to answer

Solution:

Let the tens and unit digits be x and y respectively. Then,

I. x - y = 9.

II. x + y = x - y.

From I and II, we get x - y = 9 and x + y = 9.

On solving, we get x = 9 and y = 0.

Required number is 90.

Thus, both I and II are needed to get the answer.

Correct answer is (E).

79 | S t e p U p L e a r n i n g S o l u t i o n s
 Data Interpretation

Data Interpretation involves organizing and interpreting data to get meaningful

information. It involves the use of standard and scientific methods to organize,
summarize and analyze the data.

This is usually the calculation intensive portion of the exam. It consists of a

myriad of graphs, charts and tables from which you will have to glean and
analyze data. The key to cracking this area is to quickly identify the key pieces
of data that you will require to work on the questions asked.

Problem Set 1 – Table Chart

Study the following table and answer the questions based on it.

Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years

Year Item of Expenditure

Interest
Fuel and on
Salary Transport Bonus Loans Taxes
1998 288 98 3 23.4 83
1999 342 112 2.52 32.5 108
2000 324 101 3.84 41.6 74
2001 336 133 3.68 36.4 88
2002 420 142 3.96 49.4 98

Question 1: What is the average amount of interest per year which the
company had to pay during this period?
(a) Rs. 32.43 lakhs
(b) Rs. 33.72 lakhs
(c) Rs. 34.18 lakhs
(d) Rs. 36.66 lakhs

80 | S t e p U p L e a r n i n g S o l u t i o n s
Solution
Average amount of interest paid by the Company during the given period

= Rs. 23.4 + 32.5 + 41.6 + 36.4 + 49.4 lakhs

5

= Rs. 183.3 lakhs

5

= Rs. 36.66 lakhs.

Question 2: The total amount of bonus paid by the company during the
given period is approximately what percent of the total amount of salary
paid during this period?
(a) 0.1%
(b) 0.5%
(c) 1%
(d) 1.25%

Solution

= (3.00 + 2.52 + 3.84 + 3.68 + 3.96) x 100%

(288 + 342 + 324 + 336 + 420)

= 17 x 100%
1710

= 1%. (Approx.)

Question 3: Total expenditure on all these items in 1998 was

approximately what percent of the total expenditure in 2002?

(a) 62%
(b) 66%
(c) 69%

81 | S t e p U p L e a r n i n g S o l u t i o n s
(d) 71%

Solution

= (288 + 98 + 3.00 + 23.4 + 83) x 100%

(420 + 142 + 3.96 + 49.4 + 98)

= 495.4 x 100%
713.36

= 69.45% (Approx.)

Question 4: The total expenditure of the company over these items

during the year 2000 is?

(a) Rs. 544.44 lakhs

(b) Rs. 501.11 lakhs

(c) Rs. 446.46 lakhs

(d) Rs. 478.87 lakhs

Solution

Total expenditure of the Company during 2000

= Rs. (324 + 101 + 3.84 + 41.6 + 74) lakhs

= Rs. 544.44 lakhs.

Question 5: The ratio between the total expenditure on Taxes for all the
years and the total expenditure on Fuel and Transport for all the years
respectively is approximately?

(a) 4:7

82 | S t e p U p L e a r n i n g S o l u t i o n s
(b) 10:13
(c) 15:18
(d) 5:8
Solution

Required ratio = (83 + 108 + 74 + 88 + 98)

(98 + 112 + 101 + 133 + 142)

= 451
586

= 1
1.3

= 10
13

Problem Set 2 – Bar Graph

Directions for Question 1 to 3: Refer to the following Bar-chart and answer the
questions that follow:

Question 1: What is the average value of the sales during the years
shown in the diagram?

83 | S t e p U p L e a r n i n g S o l u t i o n s
(a) Rs. 103.48 crore
(b) Rs. 105 crore
(c) Rs. 100 crore
(d) Rs.125.2 crore

Solution
(100.5 + 67 + 141 + 143.9 + 65)/5 = 103.48

Question 2: Compared to the performance in 1985 (i.e. taking it as the

base), what can you say about the performances in the years ’84, ’85,
’86, ’87, ’88 respectively, in percentage terms?

(a) 150, 100, 211, 216, 97

(b) 100, 67, 141, 144, 65
(c) 150, 100, 200, 215, 100
(d) 120, 100, 220, 230, 68

Solution

As we see the graph we see that the performance of only year i.e. 1988 is less
than the year 1985. Hence the percentage corresponding to 1988 should be less
than 100. Thus we see that (c) cannot be the answer.
Also (b) cannot be the answer as it shows two of the years having less than
100%. Between options (a) and (d), the correct answer is (a). This is because
the difference between the 1985 and 1988 performance is only 2 units on 67
units. Hence percentage-wise, it has to be 97% and not 68%.

Question 3: Which is the year in which the highest percentage decline is

seen in the value of sales achieved compared to the preceding year?

(a) 1985
(b) 1988
(c) 1984
(d) 1986

84 | S t e p U p L e a r n i n g S o l u t i o n s
Solution

The highest percentage decrease over the previous year is in year 1988, and the
performance is almost half than that of the previous year. Such a decrease is not
seen in any other year, so the right answer is b

85 | S t e p U p L e a r n i n g S o l u t i o n s
Quantitative Ability

86 | S t e p U p L e a r n i n g S o l u t i o n s
Percentages and Averages

Basic Concepts

Percentage Increase/Decrease:

1. If the value of a quantity “p” is increased by x%, the increased value is

given by,

(100 + x)
xp
X

2. If the value of a quantity “p” is decreased by x%, the decreased value is

given by,

(100 – x)
xp
X

3. If the value of a quantity is increased successively by x% and y%, the net

percentage increase is given by
(x + y + xy)/100

Average

Sum of observations
Average =
Number of observations

Example 1: A batsman scored 110 runs which included 3 boundaries and 8

sixes. What percent of his total score did he make by running between the
wickets?

Explanation:

Number of runs made by running = 110 – (3 x 4 + 8 x 6) = 110 – (60) = 50

Required percentage
50
  100  45.45.
110

Example 2: Harsh and Kylie appeared for an examination. One of them secured
9 marks more than the other and his marks was 56% of the sum of their marks.
The marks obtained by them are:

87 | S t e p U p L e a r n i n g S o l u t i o n s
Explanation:

Let their marks be (x + 9) and x.

56
Then, x + 9 = (x + 9 + x)
100

25(x + 9) = 14(2x + 9) 3x = 99 x = 33

So, their marks are 42 and 33.

Example 3: Henry had some apples. He sells 40% apples and still has 420
apples. How many fruits did he have initially?

Explanation:

Suppose originally he had x apples.

Then, (100 – 40)% of x = 420 or x = 700

Example 4: What percentage of numbers from 1 to 70 have 1 or 9 in the

unit'sdigit?

Explanation:

The unit digit of the square of the numbers that have 1 or 9 in the unit'sdigit, is
1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59,
61, 69.

Number of such number =14

14
Required percentage = x 100
70 % = 20%.

Example 5: If A = x% of y and B = y% of x, then which of the following is

true?

Explanation:

x y
x% of y = xy = xx = y% of x
100 100

A = B.

88 | S t e p U p L e a r n i n g S o l u t i o n s
Example 6: A family consists of two grandparents, two parents and three
grandchildren. The average age of the grandparents is 67 years, that of the
parents is 35 years and that of the grandchildren is 6 years. What is the
average age of the family?

Explanation:

67 x 2 + 35 x 2 + 6 x 3
Required average =
2+2+3

134 + 70 + 18
=
7

222
= years.
7

89 | S t e p U p L e a r n i n g S o l u t i o n s
 Exercise

1.While renovating his bedroom, Raj increased the length and breadth of his
bedroom by 40% each.What will be the new area of the room, measured in feet,
if its original dimensions were 144 inches by 168 inches?

(a) 12 ft x 14 ft

(b) 16.8 ft x 19.6 ft

(c) 4.8 ft x 5.6 ft

(d) 201.6 ft x 235.2 ft

2.If Soha bought a shirt for $28 after a discount of 30% was applied on it, what
was the original price of the shirt?

(a) $36.00

(b) $47.60

(c) $40.00

(d) $42.50

3. Amit appeared for 15 interviews in a month. What is the ratio between the
number of job he was not offered and the number of jobs for which he
interviewed, if he received a total of 6 job offers?

(a) 6/15

(b) 15/6

(c) 3/5

(d) 2/3

4. A television priced at $472 was sold at a discount of 30%. What was its sale
price?

(a) $141.60

(b) $225.70

90 | S t e p U p L e a r n i n g S o l u t i o n s
(c) $305.30

(d) $330.40

5. Margaret runs a nursing program where the participants are given a choice to
work with infants, elderly, or private practitioners. When given the options, 25%
of the class decided to work with infants, 60% of the class decided to work with
the elderly, 10% of the class chose to assist private practitioners, while the rest
remained undecided. What fraction of the class wanted to work with the elderly?

(a) 1/4

(b) 1/10

(c) 3/5

(d) 1/20

6. At the surgical unit in a hospital, 35% of the staff members are not available
to work during Christmas holidays. Of the remaining staff members who are
available, only 20% are certified to work. What percentage of the total staff is at
the surgical unit is both certified and available to work during the holiday
season?

(a) 7%

(b) 13%

(c) 65%

(d) 80%

7. The current dosage of a heart patient’s medication is 340 mg. After a

thorough checkup, the doctor recommended a 30% decrease in the dosage.
Thus, what is the dosage of the medication after the decrease?

(a) 70

(b) 238

(c) 270

(d) 340

91 | S t e p U p L e a r n i n g S o l u t i o n s
8. Out of the 100 patients who participated in a study about bulimia, conducted
on 100 patients, 70% of women and 10% of the men revealed they were
overweight as children. How many male patients in the study were not
overweight as children?

(a) 3

(b)10

(c) 27

(d) 30

9. Selena’s gross annual salary as the content editor of a fashion magazine is Rs.
40,000. She contributes 10% of her salary, before she pays taxes, to a
retirement account. 25% of her remaining salary is then consumed in state and
federal taxes. What is Selena’s annual take-home salary if she also has to pay
Rs.30 for health insurance each month?

(a) Rs. 2564

(b) Rs. 25970

(c) Rs.26640

(d)Rs.26970

10. Express fourteen hundredths as a percent.

(a) 0.14%

(b) 14%

(c)0.014%

(d)1.4%

11. 3 is what percent of 50?

(a) 3%

(b) 4%

92 | S t e p U p L e a r n i n g S o l u t i o n s
(c)5%

(d)6%

12. The ratio of 2:10 can also be written in percentage form as:

(a) 2%

(b) 5%

(c) 10%

(d) 20%

13.Maria made a deposit in her savings account which raised its balance from
$80 to $120. By what percentage did the total amount in her account increase
after the deposit was made?

(a) 50%

(b) 40%

(c)35%

(d) 80%

14. What is 17/68 as a percent? (Round to the nearest whole number)

(a) 17%

(b) 25%

(c)40%

(d)68%

15. Omar took 22 shots in a basketball match, out of which 13 shots were
successful. What was his shooting percentage, if rounded to the nearest whole
number?

(a) 13%

(b) 22%

(c) 59%

93 | S t e p U p L e a r n i n g S o l u t i o n s
(d) 67%

16. In a park, the lawn grass is 3 inches high. If the lawn is mowed and the
grass is cut off by 30% of its height, what is its new height?

(a) 0.9 inches

(b)2.1 inches

(c)2.7 inches

(d) 2.9 inches

17. In order for a school to allow a vending machine to be placed next to the
cafeteria, 65% of the school's population must ask for it. If 340 of the school's
650 students have requested the vending machines, how many more are needed
to get the vending machines?

(a) 75

(b) 83

(c) 89

(d) 99

18. 300roses and 750candies were purchased for Rs 5100. If the average price
of a candy was Rs.20, find the average price of a rose.

(a) 25

(b) 16

(c) 14

(d) 120

19. The wages earned by Rohit is 30% more than that earned by Erica. The
wages earned by Charles is 60% more than that earned by Erica. How much %
is the wages earned by Charles more than that earned by Rohit?

(a) 23

(b) 30

94 | S t e p U p L e a r n i n g S o l u t i o n s
(c) 40

(d) 60

20. In an election contested by two parties, Party X secured 12% of the total
votes more than Party Y. If party Y got 132,000 votes, by how many votes did it
lose the election?

(a) 40000

(b) 36000

(c) 48000

(d) 60000

Answer Key

1.b 2.c 3.c 4.d 5.c 6.b 7.b 8.c 9.c 10. b 11. d 12. d

13. a 14.b 15. b 16.b 17.b 18. d 19. a 20. b

95 | S t e p U p L e a r n i n g S o l u t i o n s
Ratio and Proportion

Ratio

The ratio of two quantities a and b, which are in the same units, is the fraction
and we write it as a : b.

In the ratio a : b, we call a as the first term or antecedent and b, the second
term or consequent.

2
Example: The ratio 2 : 3 represents with antecedent = 2, consequent = 3.
3

Proportion

The equality of two ratios is called proportion.

If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion,

where a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes.

Hence, a : b::c : d= ad : bc

Third Proportional

a : b = c : d, then c is called the third proportion to a and b.

Fourth Proportional

If a : b = c : d, then d is called the fourth proportional to a, b, c.

Mean Proportional

Mean proportional between x and y is xy.

o Duplicate ratio of (a : b) is (a2 : b2).

o Sub-duplicate ratio of (a : b) is (a : b).
o Triplicate ratio of (a : b) is (a3 : b3).
o Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).

a c a+b c+d
If = , then = . [Componendo and Dividendo]
b d a-b c-d

Example: A and B together have Rs. 1210. If of A's amount is equal to of B's
amount, how much amount does B have?

96 | S t e p U p L e a r n i n g S o l u t i o n s
Explanation:

4 2
A = B
15 5
2 15
A= x
5 4 B
3
A= B
2
A 3
=
B 2

A : B = 3 : 2.

2
B's share =1210× = Rs. 484
5

Example: Two numbers A and B are 20% and 50% more than a third number C
respectively. The ratio of the two numbers is:

Explanation:

Let C be x.

120x 6x
A = 120% of x = =
100 5
150x 3x
B = 150% of x = =
100 2
6x 3x
Ratio of A to B = : = 12x : 15x = 4 : 5.
5 2

Example: An amount is to be distributed among P, Q, R, S in the proportion of 5 : 2 : 4

: 3. If P gets Rs. 1000 more than S, what is Q's share?

Explanation:

Let the shares of P, Q, R and S be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x - 3x = 1000

x = 1000.

Q's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Example: The number of seats for subjects P, Q and R in a school is in the ratio 5 : 7 :
8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What
will be the ratio of increased seats?

Explanation:

Let the number of seats for P, Q and R initially be 5x, 7x and 8x respectively.

97 | S t e p U p L e a r n i n g S o l u t i o n s
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

140 150 175

x 5x , x 7x and x 8x
100 100 100
21x
7x, and 14x.
2
21x
The required ratio = 7x : : 14x
2

14x : 21x : 28x

2 : 3 : 4.

Example:In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 :
2, then the quanity of water to be further added is:

Explanation:

2
Quantity of milk = 60 × = 40 liters
3

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

40
Then, milk : water = .
20 + x
40 1
Now, =
20 + x 2

20 + x = 80

x = 60.

Quantity of water to be added = 60 litres

Example: The ratio of the number of mangoes and bananas in a bag is 7 : 8. If the
percentage increase in the number of mangoes and bananas be 20% and 10%
respectively, what will be the new ratio of mangoes to bananas in the bag?

Explanation:

Originally, let the number of mangoes and bananas in the college be 7x and
8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

98 | S t e p U p L e a r n i n g S o l u t i o n s
 120 110
x 7x and x 8x
100 100
42x 44x
and
5 5
42x 44x
The required ratio = : = 21 : 22
5 5

7Example: The salaries of Sakshi and Sumit are in the ratio 2 : 3. If the salary of each is
.increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

Explanation:

Let the original salaries of Sakshi and Sumit be Rs. 2x and Rs. 3x respectively.

2x + 4000 40
Then, =
3x + 4000 57

57(2x + 4000) = 40(3x + 4000)

6x = 68,000

3x = 34,000

Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000

Example: The sum of ages of three persons is 98. If the ratio of the first to second is
2 :3 and that of the second to the third is 5 : 8, then the age of the second person is

Explanation:

Let the ages of three persons be A, B, C.

3 3 24
A : B = 2 : 3 and B : C = 5 : 8 = 5x : 8x =3:
5 5 5
24
A:B:C=2:3: = 10 : 15 : 24
5
15
B= 98 x = 30.
45

Example: If Rs. 782 be divided amongs three persons in the ratio : : , what is
the first part?

Explanation:

Given ratio = : : = 6 : 8 : 9.

99 | S t e p U p L e a r n i n g S o l u t i o n s
 2
1st part = 60   40.
3

.Example: The salaries Ankur, Bindu and Chiku are in the ratio 2 : 3 : 5. If the
increments of 15%, 10% and 20% are allowed respectively in their salaries, then what
will be new ratio of their salaries?

Explanation:

Let the salaries of Ankur, Bindu and Chiku be 2k, 3k and 5k respectively.

115 115 23k

Ankur's new salary = of 2k = x 2k =
100 100 10
110 110 33k
Bindu's new salary = of 3k = x 3k =
100 100 10
120 120
Chiku's new salary = of 5k = x 5k = 6k
100 100
23k 33k
New ratio : 6k = 23 : 33 : 60
10 10
Example: If 40% of the number of students in one class is equal to two-third of the
number of students in another class, what is the ratio of number off studenst in the first to
that in the second class?

Explanation:

Let the number of students in the two classes be A and B.

2 2 2
40% of A = B  A = B = A : B = 5 : 3.
3 5 3

Example: What is the fourth proportional to 5, 8, 15

Explanation:

Let the fourth proportional to 5, 8, 15 be x.

Then, 5 : 8 : 15 : x

5x = (8 x 15) x = 24.

Example: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If

there is Rs. 30 in all, how many 5 p coins are there?

Explanation:

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.

100 | S t e p U p L e a r n i n g S o l u t i o n s
 25x 10 x 2x 5 x 3x 60x
Then, sum of their values = Rs. + + = Rs.
100 100 100 100
60x 30 x 100
= 30 x= = 50.
100 60

Hence, the number of 5 p coins = (3 x 50) = 150.

101 | S t e p U p L e a r n i n g S o l u t i o n s
 Exercise

1. A sum of 120 is divided in the ratio 3:4:5. What is the largest share?

(a)10

(b)30

(c)50

(d) 55

2.Find the largest share when Rs. 192.50 is divided in the ratio of 2:5.

(a)55

(b)27.5

(c)137.50

(d) 90

3.Find the smallest share when 260g is divided in the ratio of 4:2:7.

(a)20g

(b)140g

(c)40g

(d) 60g

4. Reduce the following fraction to the simplest possible ratio: 8/14

(a) 4:3 (b) 4:6 (c)4:7 (d)3:4

5. If 5 people buy 3 cupcakes each and 3 people buy 7 cookies each, what is the
ratio of the total number of cupcakes to the total number of cookies?

(a) 15 :21 (b) 3:7 (c) 5:3 (d) 1:1

6. In a university, the ratio of male students to female students is 2:1. If the

number of female students in the town is doubled, what will be the new ratio of
females to males?

102 | S t e p U p L e a r n i n g S o l u t i o n s
(a) 1:2

(b) 1:1

(c) 2:1

(d) 3:1

7. Two numbers are in the ratio of 3:5. If 9 be subtracted from each,they are in
the ratio of 12:23.The first number is:

(a) 27

(b) 33

(c)55

(d)49

8.If a 13 m-long iron rod weighs 23.4 kg, then how much would a 6 m-long iron
rod weigh?

(a) 7.2 kg

(b) 12.4 kg

(c) 10.8 kg

(d)18 kg

9.The ratio of two numbers is 3:8 and their difference is 115.The greater number
is:

(a)69

(b)115

(c)184

(d)230

10. Half of one number is equal to 0.07 of another. The ratio of the numbers is:

(a)50:7

103 | S t e p U p L e a r n i n g S o l u t i o n s
(b)5:7

(c) 7:50

(d)1:14

11. In a box, 25 paise, 10 paise, and 5 paise coins are in the ratio of 1:2:3.If
their total value is Rs 30, then the number of 5 paise coins is:

(a)50

(b)100

(c)150

(d)200

12. Mr. Singh divided his property such that the ratio of his son’s share to his
wife’s and the ratio of the wife’s share to his daughter are both 3:1.If the
daughter gets Rs. 10,000 less than the son, then what is the total worth of the
property?

(a) Rs. 25000

(b) Rs. 16250

(c) Rs. 65000

(d) Rs. 27350

13. A 20-liter mixture of milk and water contains milk and water in the ratio 3:
2. 10 liters of the mixture is removed and replaced with pure milk and the
operation is repeated once more. At the end of the two removal and
replacement, what is the ratio of milk and water in the resultant mixture?

(a) 17: 3

(b) 9 : 1

(c) 3 : 17

(d) 5 : 3

104 | S t e p U p L e a r n i n g S o l u t i o n s
14.In what ratio must a person mix three kinds of tea costing Rs.60/kg,
Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.96/kg
yields a profit of 20%?

(a)1:2: 4

(b) 3:7: 6

(c) 1:4: 2

(d) 3: 9: 6

15.How many liters of water should be added to a 30-liter mixture of milk and
water containing milk and water in the ratio of 7: 3 such that the resultant
mixture has 40% water in it?

(a) 7 liters

(b) 10 liters

(c) 5 liters

(d) None of these

Answer Key

1.c 2.c 3.c 4.c 5.a 6.b 7.b 8.c 9.c 10.c 11.c 12.c
13.b 14.c 15.b

105 | S t e p U p L e a r n i n g S o l u t i o n s
Simple Interest and Compound Interest

Principal

The money borrowed or lent for a certain period of time is called the principal or
the sum.

Interest

Extra money paid for using other's money is called interest.

Simple Interest (S.I.)

If the interest is calculated every year or every time period on the principal or the sumat
the beginning of first year, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years.

PxRxT
(i). Simple Interest =
100
100 x S.I. 100 x S.I. 100 x S.I.
(ii). P = ;R= and T = .
RxT PxT PxR

Compound Interest (C. I.)

In case of compound interest, principal keeps changing. The principal at a beginning of

particular period is the sum of the principal at the beginning of the previous period and
the interest accrued in that period.

Let Principal = P, Rate = R% per annum, Time = n years.

When interest is compound Annually:

R n
Amount = P 1+
100

When interest is compounded half-yearly:

(R/2) 2n
Amount = P 1+
100

When interest is compounded quarterly:

(R/4) 4n
Amount = P 1 + 100
100 100

106 | S t e p U p L e a r n i n g S o l u t i o n s
When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and
3rd year respectively:

R1 R2 R3
Amount = P 1+ 1+ 1+ .
100 100 100

Present worth of Rs. x due n years hence is given by

x
Present Worth = R .
1+
100

Example: A sum of money at simple interest amounts to Rs. 815 in 3 years and to
Rs.854 in 4 years. What is the sum?

Explanation:

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.

Example: Mr. Arkur invested an amount of Rs. 139000 divided in two different schemes
S1 and S2 at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total
amount of simple interest earned in 2 years be Rs. 35080, what was the amount
invested in Scheme S2?

Explanation:

Let the sum invested in Scheme S1 be Rs. x and that in Scheme S2 be Rs. (139000 - x).

x x 14 x 2 (139000 - x) x 11 x 2
Then, + = 35080
100 100

28x - 22x = 3508000 - (139000 x 22)

6x = 450000

x = 75000.

So, sum invested in S2 = Rs. (139000 - 75000) = Rs. 64000.

3
Example: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in
5 years. What is the sum?

Explanation:

100 x 4016.25
= Rs.
Principal 9x5

107 | S t e p U p L e a r n i n g S o l u t i o n s
 401625
= Rs.
45

= Rs. 8925

Example: Reena took a loan of Rs. 1200 at simple interest for as many years as the
rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was
the rate of interest?

Explanation:

Let rate = R% and time = R years.

1200 x R x R
Then, = 432
100

12R2 = 432

R2 = 36

R = 6.

Example: Raj claims to be lending money at simple interest, but he includes the
interest every six months for calculating the principal. If he is charging an interest of
10%, the effective rate of interest becomes:

Explanation:

Let the sum be Rs. 100.

100 x 10 x 1
S.I. for first 6 months = Rs. = Rs. 5
100 x 2
105 x 10 x 1
S.I. for last 6 months = Rs. = Rs. 5.25
100 x 2

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 - 100) = 10.25%

Example: P lent Rs. 5000 to Q for 2 years and Rs. 3000 to R for 4 years on simple
interest at the same rate of interest and received Rs. 2200 in all from both of them as
interest. What is the rate of interst?

Explanation:

Let the rate be r% p.a.

108 | S t e p U p L e a r n i n g S o l u t i o n s
 5000 x r x 2 3000 x r x 4
+ = 2200.
100 100

100r + 120r = 2200

2200
r= = 10.
220

Example: Arpit borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He

immediately lends it to another person at 6 p.a for 2 years. Find his gain in the
transaction per year.

Explanation:

Gain in 2 25 2 5000 x 4 x 2
= 5000 x x –
years 4 100 100

= (625 - 400)

= Rs. 225.

225
Gain in 1 year = = Rs. 112.50
2

Example: The difference between simple and compound interests compounded annually
on a certain sum of money for 2 years at 4% per annum is Re. 10. The sum (in Rs.) is:

Explanation:

Let the sum be Rs. x.

4 2 676 51
C.I. = x 1 + 100 -x = 625x - x = 625x.

xx4x2 2x
S.I. = = .
100 25
51x 2x
- = 10
625 25

x = 6250.

5
Example: In how many years the compound interest on Rs. 30,000 at 7% per annum is
Rs. 4347?:

Explanation:

Amount = Rs. (30000 + 4347) = Rs. 34347.

109 | S t e p U p L e a r n i n g S o l u t i o n s
Let the time be n years.

7 n
Then, 30000 1+ = 34347
100
107 n 34347 11449 107 2
= = =
100 30000 10000 100

n = 2 years.

Example: What will be the compound interest on a sum of Rs. 25,000 after 3 years at
the rate of 12 p.c.p.a.?

Explanation:

12 3
Amount = Rs. 25000 x 1 + 100

28 28 28
= Rs. 25000 x x x
25 25 25

= Rs. 35123.20

C.I. = Rs. (35123.20 - 25000) = Rs. 10123.2

Example: At what rate of compound interest per annum will a sum of Rs. 1200 become
Rs. 1348.32 in 2 years?

Explanation:

Let the rate be R% p.a.

R 2 R 2 134832 11236
Then, 1200 x 1+ = 1348.32 1+ = =
100 100 120000 10000

R 106
1+ =
100 100

R = 6%

Example: The least number of complete years in which a sum of money put out at 20%
compound interest will be more than doubled is:
Explanation:

20 n 6 n
P 1+ > 2P > 2.
100 5
6 6 6 6
Now, x X x > 2.
5 5 5 5

So, n = 4 years.

110 | S t e p U p L e a r n i n g S o l u t i o n s
Exercise

1.A bank offers 5% compound interest calculated on half-yearly basis. Suresh

deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the
year, the amount he would have gained by way of interest is:

(a) Rs. 120

(b) Rs. 121

(c) Rs.122

(d) Rs.123

2.The difference between simple and compound interests compounded annually

on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in
Rs.) is:

(a) Rs. 625

(b) Rs. 630

(c) Rs. 640

(d) Rs.650

3. There is 60% increase in an amount in 6 years at simple interest. What will

be the compound interest of Rs. 12,000 after 3 years at the same rate?

(a) Rs. 2160 .

(b) Rs. 3120

(c) Rs. 3972

(d) Rs. 6240

(e) None of these

4. What is the difference between the compound interests on Rs. 5000 for 1
years at 4% per annum compounded yearly and half-yearly?

(a) Rs. 2

111 | S t e p U p L e a r n i n g S o l u t i o n s
(b) Rs. 3

(c) Rs. 4

(d) Rs. 8

5. What will be the compound interest on a sum of Rs. 25,000 after 3 years at
the rate of 12 p.c.p.a.?

(a) Rs. 9000.30

(b) Rs. 9720

(c) Rs. 10123.20

(d) Rs. 10483.20

6. At what rate of compound interest per annum will a sum of Rs. 1200 become
Rs. 1348.32 in 2 years?

(a) 6%

(b) 6.5%

(c) 7%

(d) 7.5%

7. The least number of complete years in which a sum of money put out at 20%
compound interest will be more than doubled is:

(a) 3

(b) 4

(c) 5

(d) 6

8. Sneha invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years
at compound interest rate 5 p.c.p.a. How much amount will Sneha get on
maturity of the fixed deposit?

(a) Rs. 8600

112 | S t e p U p L e a r n i n g S o l u t i o n s
(b) Rs. 8620

(c) Rs. 8820

(d) None of these

9. The effective annual rate of interest corresponding to a nominal rate of 6%

per annum payable half-yearly is:

(a) 6.06%

(b) 6.07%

(c) 6.08%

(d) 6.09%

10. Simple interest on a certain sum of money for 3 years at 8% per annum is
half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum
placed on simple interest is:

(a) Rs. 1550

(b) Rs. 1650

(c) Rs. 1750

(d) Rs. 2000

11. If the simple interest on a sum of money for 2 years at 5% per annum is Rs.
50, what is the compound interest on the same at the same rate and for the
same time?

(a) Rs. 51.25

(b) Rs. 52

(c)Rs. 54.25

(d) Rs. 60

12. The difference between simple interest and compound on Rs. 1200 for one
year at 10% per annum reckoned half-yearly is:

113 | S t e p U p L e a r n i n g S o l u t i o n s
(a) Rs. 2.50

(b) Rs. 3

(c). Rs. 3.75

(d) Rs. 4

13. The difference between compound interest and simple interest on an amount
of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

(a) 8

(b) 10 .

(c) 12

(d) Cannot be determined

14.The compound interest on a certain sum for 2 years at 10% per annum is Rs.
525. The simple interest on the same sum for double the time at half the rate
percent per annum is:

(a) Rs. 400

(b) Rs. 500

(c) Rs. 600

(d) Rs. 800

Answer key

1. c 2.a 3.c. 4.a 5.c 6.a 7.b 8.c 9.d 10.c 11.a 12.b
13.a 14.b

114 | S t e p U p L e a r n i n g S o l u t i o n s
Speed, Time & Distance

Basic Concepts

1. Speed, Time and Distance:

Distance Distance
Speed = , Time = , Distance = (Speed x Time).
Time Speed

2. km/hr to m/sec conversion:

5
x km/hr = xx m/sec.
18

3. m/sec to km/hr conversion:

18
x m/sec = xx km/hr.
5

4. If the ratio of the speeds of A and B is a : b, then the ratio of the

1 1
the times taken by then to cover the same distance is : or b : a.
a b

5. Suppose a man covers a certain distance at x km/hr and an equal

distance at y km/hr. Then,

2xy
the average speed during the whole journey is km/hr
x+y

1Example:A person crosses a 600 m long street in 5 minutes. What is his speed
.in km per hour?

Explanation:
600
Speed =
m/sec.
5 x 60

= 2 m/sec.

18
= 2x km/hr
5

= 7.2 km/hr

115 | S t e p U p L e a r n i n g S o l u t i o n s
Example:An train covers a certain distance at a speed of 240 kmph in 5 hours.

To cover the same distance in 1 hours, it must travel at a speed at

Explanation:

Distance = (240 x 5) = 1200 km.

Speed = Distance/Time

Speed = 1200/(5/3) km/hr

3
Required speed = 1200 x = 720 km/hr

Example: If a lady walks at 14 km/hr instead of 10 km/hr, she would have

walked 20 km more. What is the actual distance travelled by her?

Explanation:

Let the actual distance travelled be x km.

x x + 20
=
10 14

14x = 10x + 200

4x = 200

x = 50 km

5Example: Excluding stoppages, the speed of a bus is 54 kmph and including

.stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Explanation:

Due to stoppages, it covers 9 km less.

9
Time taken to cover 9 km = x 60 = 10 min.
54

Example: During a journey of 600 km, an aircraft was slowed down due to bad
weather, due to which its average speed for the trip was reduced by 200 km/hr
and the travel time was increased by 30 minutes. The duration of the journey is

Explanation:

116 | S t e p U p L e a r n i n g S o l u t i o n s
Let the duration of the flight be x hours.

600 600
Then, - = 200
x x + (1/2)
600 1200
- = 200
x 2x + 1

x(2x + 1) = 3

2x2 + x - 3 = 0

(2x + 3)(x - 1) = 0

x = 1 hr.

7Example: A man complete a journey in 10 hours. He travels first half of the

.journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find
the total journey in km.

Explanation:

(1/2)x (1/2)x
+ = 10
21 24
x x
+ = 20
21 24

15x = 168 x 20 x =224 km.

Example: A bile running with of its actual speed covers 42 km in 1 hr 40 min

48 sec. Find the actual speed of the bike.

Explanation:

4 51 126
Time taken = 1 hr 40 min 48 sec = 1 hr 40 min = 1 hrs = hrs.
5 75 75

Let the actual speed be x km/hr.

5 126
Then, xx = 42
7 75
42 x 7 x 75
x= = 35 km/hr.
5 x 126

117 | S t e p U p L e a r n i n g S o l u t i o n s
Exercise

1. An ant moves at a distance of 45cm in 90 seconds. Find the speed of the ant.

(a) 2 cm/s

(b) 0.5 cm/s

(c) 4050 cm/s

(d) 1cm/s

2.A car leaves Delhi at 8.00am and arrives in Jaipur at 10.30am. If the distance
is 120 km, find the average speed.

(a) 300 km/hr

(b) 60 km/hr

(c) 48 km/hr

(d) 24km/hr

3.A crocodile, attacking a boat, swims at a speed of 13m/s for half a minute.
How far does it swim in this time?

(a) 390 m

(b) 6.5 m

(c) 0.43 m

(d) 4.8m

4.A car leaves Udaipur at 8.30am and arrives in Jaisalmer at 5.30pm. If the car
travels at an average speed of 75 km/hr, how far is it from Udaipur to Jaisalmer?

(a) 8.3 km

(b) 600 km

(c) 675 km

(d) 800 km

118 | S t e p U p L e a r n i n g S o l u t i o n s
5.A car travels at 88 km/hr over a distance of 22 km. Find in minutes the time
taken for the car to travel this distance.

(a) 4 minutes

(b) 15 minutes

(c) 240 minutes

(d) 80 minutes

6.A car travelling at a steady speed takes 4 hours to travel 244 km. Find the
average speed of the car.

(a) 976 km/hr

(b) 61 km/hr

(c) 0.02 km/hr

(d) 44k/hr

7.A bus travels at a constant speed of 40 mph for 3 hours. How far does the car
go?

(a) 120 mph

(b) 0.075 mph

(c) 13.3 mph

(d) 4.6mph

8.An octopus swims 7 km at a speed of 3 km/hr. How long does it take in hours
and minutes?

(a) 2 hours 33 mins

(b) 2 hours 20 mins

(c) 0 hours 41 mins

(d) 5 hours 45 mins

9.A hyena runs for 2 hours 15 mins at a speed of 8 mph. How far does it run?

119 | S t e p U p L e a r n i n g S o l u t i o n s
(a) 17.2 miles

(b) 3.6 miles

(c) 18 miles

(d) 16.5 miles

10. The distance from Patna to Bodhgaya by rail is 420km. At what average
speed must a train travel to cover this distance in 4 hours?

(a) 105 km/hr

(b) 1680 km/hr

(c)1050 km/hr

(d) 1430 km/hr

11: A train traveling at 72 kmph crosses a platform in 30 seconds and a man

standing on the platform in 18 seconds. What is the length of the platform in
meters?

(a)310kmph

(b) 440

(c) 550

(d) 75

12: A train traveling at 100 kmph overtakes a car traveling at 64 kmph in 40

seconds. What is the length of the train in meters?

(a)215kmph

(b) 400kmph

(c) 360 kmph

(d) 80kmph

120 | S t e p U p L e a r n i n g S o l u t i o n s
13: Jim travels the first 3 hours of his journey at 60 mph speed and the
remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in
mph?

(a) 43.8 mph

(b) 65 mph

(c) 37.5 mph

(d) 43.5 mph

14: A runs 25% faster than B and is able to give him a start of 7 meters to end
a race in dead heat. What is the length of the race?

(a) 84m

(b)18m

(c) 47 m

(d)Cannot be determined

15: Jane covered a distance of 340 miles between city A and city taking a total
of 5 hours. If part of the distance was covered at 60 miles per hour speed and
the balance at 80 miles per hour speed, how many hours did she travel at 60
miles per hour?

(a) 14 hours

(b) 4hours

(c) 12 hours

(d) 3 hours

Answer Key

1. b 2.c 3.b 4.c 5.c 6.b 7.a 8.b 9.c 10.a 11.b 12.b 13.c
14.d 15.d

121 | S t e p U p L e a r n i n g S o l u t i o n s
Time and Work

• If P can do a piece of work in x days, the work done by P in a 1 day is 1/x.

• If P's work efficiency is 3 times as compared to Q, ratio of work done by P and Q
is 3 :1and the ratio of times taken by P and Q to finish a work is 1 : 3 (inverse
ratio of work done)
• If a group of people work together on a task, it is assumed that all people are of
the same efficiency unless it is specified otherwise.
• Let M1 person can do W1 work in D1 days working for T1 unit of time daily and
M2 person can do W2 work in D2 days working for T2 unit of time daily, then the
relationship can be written as:

• If P and Q can do a work in x and y days respectively, then they working

xy
together can finish the work in days.
x+y
Example: If 30 men working together can complete a piece of work in 10 days
by working 8 hours daily, in how many days can 20 men working together can
complete the same work by working 10 hours daily ?

Solution: Let the required number of days be ‘x’.

By using M1D1H1 = M2D2H2, we will get

30 × 10 × 8 = 20 × x × 10 or x =12.
Example: A does a work in 10 days and B does the same work in 15 days. In
how many days they together will do the same work?
Solution:

So both will finish the work in 6 days

Inlet: A pipe connected with a tank or a cistern or a reservoir that fills it, is
known as an inlet.
Outlet: A pipe connected with a tank or cistern or reservoir that empties it, is
known as an outlet.
1
• If a pipe can fill a tank in x hours, then part filled in 1 hour is 1/x .
x
• If a pipe can empty a tank in y hours, then part emptied in 1
hour is 1/y.

1. If a pipe can fill a tank in x hours and another pipe can empty the full tank
in y hours (where y > x), then on opening both the pipes,

1 1
the net part filled in 1 hour = - .
x y

2. If a pipe can fill a tank in x hours and another pipe can empty the full tank
in y hours (where x > y), then on opening both the pipes

122 | S t e p U p L e a r n i n g S o l u t i o n s
 1 1
the net part emptied in 1 hour = - .
y x

Example: pump can fill a tank with water in 2 hours. Because of a leak, it took 2
hours to fill the tank. The leak can drain all the water of the tank in:

Explanation:

1 3 1
Work done by the leak in 1 hour = - = .
2 7 14

Leak will empty the tank in 14 hrs

Example: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes
respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B
is turned off after:

Explanation:

Let B be turned off after x minutes. Then,

Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.

2 1 2
x + + (30 - x). =1
75 45 75
11x (60 -2x)
+ =1
225 75

11x + 180 - 6x = 225.

x=9

Example:Three pipes are two fill a tank. The first two pipes operating simultaneously fill
the tank in the same time that the third takes alone. The second pipe takes 5
hours less than the first pipe and 4 hours more than the third pipe to fill the
tank. The time taken by the first pipe is:

Explanation:Let the first pipe alone takes x hours to fill the tank.

Therefore, the second and third pipes will take (x -5) and (x - 9) hours respectively to fill
the tank.

1 1 1
+ =
x (x - 5) (x - 9)
x-5+x 1
=
x(x - 5) (x - 9)

123 | S t e p U p L e a r n i n g S o l u t i o n s
 (2x - 5)(x - 9) = x(x - 5)

x2 - 18x + 45 = 0

(x - 15)(x - 3) = 0

x = 15. [x = 3 is not possible]

6Example: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe
.can empty 3 gallons per minute. All the three pipes working together can fill the tank in
15 minutes. The capacity of the tank is:

Explanation:

1 1 1
Work done by the waste pipe in 1 minute = - +
15 20 24
1 11
= -
15 120
1
=- . [-ve sign means emptying]
40
1
Volume of part = 3 gallons.
40

Volume of whole = (3 x 40) gallons = 120 gallons.

7Example: A vessel is filled in 5 hours by three pipes P, Q and R. The pipe C is twice as
.fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the
tank?

Explanation:

Suppose pipe A alone takes x hours to fill the tank.

x x
Then, pipes B and C will take and hours respectively to fill the tank.
2 4
1 2 4 1
+ + =
X x x 5

x = 35 hrs.

8Example:Two pipes A and B together can fill a cistern in 4 hours. Had they been opened
.separately, then B would have taken 6 hours more than A to fill the cistern. How much
time will be taken by A to fill the cistern separately?

Explanation:

Let the cistern be filled by pipe A alone in x hours.

124 | S t e p U p L e a r n i n g S o l u t i o n s
Then, pipe B will fill it in (x + 6) hours.

1 1 1
+ =
x (x + 6) 4
x+6+x 1
=
x(x + 6) 4

x2 - 2x - 24 = 0

(x -6)(x + 4) = 0

x = 6. [neglecting the negative value of x]

Example:Two taps P and Q can fill a tank in 15 minutes and 20 minutes respectively.
Both the pipes are opened together but after 4 minutes, pipe P is turned off. What is the
total time required to fill the tank?

Explanation:

1 1 7
Part filled in 4 minutes = 4 + = .
15 20 15
7 8
Remaining part = 1- = .
15 15
1
Part filled by B in 1 minute =
20
1 8
: :: 1 : x
20 15
8 2
x= x 1 x 20 = 10 min = 10 min. 40 sec.
15 3

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.

125 | S t e p U p L e a r n i n g S o l u t i o n s
Exercise

1. Two workers A and B manufactured a batch of identical parts. A worked for 4

hours and B worked for 10 hours and they did half the job. Then they worked
together for another 6 hours and they had to do (1/20)th of the job. How much
time does B take to complete the job, if he worked alone?

(a) 24 hours

(b) 12 hours

(c) 15 hours

(d) 30 hours

2. Pipe A can fill a tank in 3 hours. On account of a leak at the bottom of the
tank it takes thrice as long to fill the tank. How long will the leak at the bottom
of the tank take to empty a full tank, when pipe A is kept closed?

(a) (9/2) hours

(b) (10/3) hours

(c) (13/3) hours

(d) (13/4) hours

3. A and B working together can finish a job in T days. If A works alone and
completes the job, he will take T + 5 days. If B works alone and completes the
same job, he will take T + 45 days. What is T?

(a) 25

(b) 60

(c) 15

(d) None of these

4. A man can do a piece of work in 60 hours. If he takes his son with him and
both work together then the work is finished in 40 hours. How long will the son
take to do the same job, if he worked alone on the job?

126 | S t e p U p L e a r n i n g S o l u t i o n s
(a) 0 hours

(b) 120 hours

(c) 24 hours

(d) None of these

5. A, B and C can do a work in 5 days, 10 days and 15 days respectively. They

started together to do the work but after 2 days, A and B left. C did the
remaining work in

(a) 1 days

(b) 3 days

(c) 5 days

(d) 4 days

6. X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X

and Y undertook to do it for Rs.720. With the help of Z they finished it in 5 days.
How much is paid to Z?

(a) Rs.360

(b) Rs.120

(c) Rs.240

(d) Rs.300

7. Ram starts working on a job and works on it for 12 days and completes 40%
of the work. To help him complete the work, he employs Ravi and together they
work for another 12 days and the work gets completed. How much more
efficient is Ram than Ravi?

(a) 50%

(b) 200%

(c) 60%

(d)100%

127 | S t e p U p L e a r n i n g S o l u t i o n s
8. P and Q can do a piece of work in 21 and 24 days respectively. They started
the work together and after some days P leaves the work and Q completes the
remaining work in 9 days. After how many days did P leave?

(a) 5

(b) 7

(c) 8

(d) 6

9. Raj, who is half as efficient as Krish, will take 24 days to complete a work if
he worked alone. If Raj and Krish worked together, how long will they take to
complete the work?

(a) 16 days

(b) 12 days

(c) 8 days

(d) 18 days

10.A completes a work in 12 days and B complete the same work in 24 days. If
both of them work together, thenthe number of days required to complete the
work will be

(a) 8 days

(b) 6 days

(c) 7 days

(d) 5 days

11. If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m
long cloth in how many days

(a) 1 days

(b) 1 ½ days

(c) ¾ day

128 | S t e p U p L e a r n i n g S o l u t i o n s
(d) ½ day

12.If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons

can do 7 times of that work in

(a) 7 days

(b) 6 days

(c) 4 days

(d) 3 days

13.Manu completes a piece of work in 10 days,Raju completes the same work in

40 days. If both of them work together, then the number of days required to
complete the work is

(a) 15 days

(b) 10 days

(c) 9 days

(d) 8 days

14.12 men work 8 hours per day to complete the work in 10 days. To complete
the same work in 8 days,working 15 hours a day, the number of men required

(a) 4 days

(b) 5 days

(c) 6 days

(d) 8 days

15.If 5 people undertook a piece of construction work and finished half the job in
15 days. If two people drop out, then the job will be completed in

(a) 25 days

(b) 20 days

(c) 15 days

129 | S t e p U p L e a r n i n g S o l u t i o n s
 (d) 10 days

Answer Key:

1. a 2. b 3. c 4. b 5. d 6. b 7. d 8. b 9.c 10.a 11. a 12. a

13.d 14. a 15. a

130 | S t e p U p L e a r n i n g S o l u t i o n s

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