MATH

OLYMPIAD
P R A C T I C E W O R K S H E E T S

GRADE 7
SOF IMO EXAM FORMAT
WITH DETAILED SOLUTIONS
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IMO Mock Test CLASS

7
PATTERN & MARKING SCHEME

(1) Logical (2) Mathematical (3) Everyday (4) Achievers

Section Reasoning Reasoning Mathematics Section

No. of Questions 15 20 10 5

Marks per 1 1 1 3
Question

LOGICAL REASONING

(1) Arrange the following words in their dictionary order:

1. HOWJHS 2. HOYJHS 3. HOWMHS 4. HOWJJS

a. 4 1 3 2 b. 1 4 3 2
c. 1 4 2 3 d. 1 3 4 2

(2) Pointing towards a man playing cricket, Gita says, "He is the brother of my uncle's daughter". How
is the man related to Gita?
a. Cousin b. Brother-in-law
c. Uncle d. Son

(3) Priyanka is standing in a row. If she is 18th from the front and 27th from the back, how many
people are standing in the row ?
a. 46 b. 44
c. 45 d. 43

(4) How many triangles are there in the figure below ?

a. 15 b. 19
c. 17 d. 13

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(5) In a magic square, the rows, the columns and the diagonals each add up to the same number. In
this magic square, the numbers 43, 44, 23, 65, 33, and 1 are missing.

22 q 12

p b r

54 x z

What will be the value of q ?

a. 65 b. 75
c. 72 d. 70

(6) In a magic square, the rows, the columns and the diagonals each add up to the same number. In
the given magic square, the numbers 70, 38, 43, 48, 16, and 54 are missing.

32 a 27

b y c

59 q x

What is the value of c + q in the given magic square?

a. 72 b. 69
c. 64 d. 74

(7) If the reflection of a clock in mirror shows time as 1:15, find the actual time.
a. 1:15 b. 11:45
c. 10:15 d. 10:45

(8) Find the missing term.

a. 14 b. 12
c. 15 d. 16

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(9) How many times do a clock's hour and minute hands overlap in a day?
a. 22 b. 24
c. 21 d. 20

(10) - =9 > 13 <6

Find the value of

a. 12 b. 16
c. 13 d. 14

(11) Sarika decided to choose 1 animal, 1 plant and 1 flower sticker from each of the sticker groups, as
shown, to decorate her drawing notebook. Which of the following represents the total number of
different combinations of stickers that Sarika can choose?

Animals

Plants

Flowers

a. 48 b. 45
c. 16 d. 12

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(12) Find the value of missing numbers A and B in the following pattern.
256
B 144

48 64 80

20 28 36 A
8 12 16 20 24

3 5 7 9 11 13

1 2 3 4 5 6 7

a. 45,112 b. 44,112
c. 45,113 d. 44,113

(13) In a month of 30 days, it is Wednesday on a given date of the month. Find the day on the same
date of the next month.
a. Saturday b. Friday
c. Wednesday d. Thursday

(14) ●●●+♦♦=♦♦♦♦♦♦♦♦
Based on the above condition, which of the following statements is true?

a. ●=♦♦♦ b. ●=♦♦
c. ● = ♦ d. ● = ♦ ♦ ♦ ♦

(15) = - 2

+ + = 39

+ + + + =?

a. 55 b. 57
c. 56 d. 53

MATHEMATICAL REASONING

2 2 2
1 2 −2
(16) ( ) × ( ) × ( ) = ?
2 3 2

6
a. b. 10
9

1 10
c. d.
9 14

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(17) If ∠BDC and ∠ACB are right angles, what is the measure of ∠CBD ?

a. 40° b. 50°
c. 55° d. 45°

2 2
(18) In a race, Sarika has covered of the total distance, whereas, Sita has covered only . How
5 7

much less distance has Sita covered as compared to Sarika?

1 6
a. b.
7 35

1 4
c. d.
5 35

(19) Rohit is Sita's brother, Sita is Pradip's sister, and Pradip is Madhav's father. Who is Madhav to
Rohit?
a. Niece b. Aunt
c. Brother d. Uncle

(20) If the distance between A and C is 91 meters, find the distance between B and D.

a. 109 meters b. 114 meters

c. 118 meters d. 104 meters

(21) The population of a town increased by 2% in the first year. The next year, it decreased by 10%
and became 8262. What was the population of the town at the beginning of the first year?
a. 8950 b. 8940
c. 9000 d. 9010

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(22) The radius of a wheel of a truck is 26.6 cm. If the wheel makes 2000 rotation in one minute, how
far will the truck travel in 30 minutes? (assume π = 22/7)
a. 90.29 km b. 110.35 km
c. 80.26 km d. 100.32 km

(23) In an exam of History and General Knowledge, 32% and 39% students failed in History and
General Knowledge respectively. If 16% students failed both in History and General Knowledge,
find the percentage of students who passed in both the exams.
a. 38% b. 48%
c. 41% d. 45%

(24) If, = 20
= 18

= 20

= 28

Find the value of .

a. 38 b. 37
c. 36 d. 39

4 8
(25) If th part is equal to 8, then th part is equal to:
8 8
a. 8 b. 29
c. 16 d. 25

(26) How many edges does a triangular pyramid have?

a. 6 b. 4
c. 5 d. 8

(27) Find the order of rotational symmetry in the given image.

a. 6 b. 5
c. 4 d. 8

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(28) The value of:

1
1 +
1
1 +
8

is
17 9
a. b.
9 17

17
c. 1 + d. None of these
9

(29) Which figure has fewer faces?

(30) If the number in the center is the sum of rest of the numbers, find the value of y.

a. 2 b. 3
c. 1 d. 0

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(31) The following bar chart shows the number of fruits in a shop.

60

Number of fruits 50

40

30

20

10

0
Orange Pear Papaya Guava Pineapple

Fruits
How many more pears are there than guavas?
a. 20 b. 40
c. 10 d. 30

(32) Aditya is in the process of making ice cream. He has heated all the ingredients to 60 C and put
∘

them in a refrigerator to freeze. If the cooling rate is 10∘ C per hour, what will be the temperature
in the freezer after 11 hours?
a. 170 b. −50
∘ ∘
C C

c. −170 d. 50
∘ ∘
C C

(33) In a month of 31 days, it is Tuesday on a given date of the month. Find the day on the same date
of the next month.
a. Wednesday b. Saturday
c. Thursday d. Friday

(34) If x is an integer, which of following must be an odd integer?

a. x3 + 9 b. 46x3 + 9
c. 9x + 46 d. 9x

(35) Which of the following is a possible length for side AB of a triangle ABC, if AC = 5 and BC = 9?
I. 6
II. 15
III. 2

a. II only b. II and III

c. I only d. I, II and III

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EVERYDAY MATHEMATICS

(36) George had some boxes of cards (each box contains 19 cards). He gave away 27 cards to his
friend Sulekha. If p is the number of boxes George originally had, how many cards are left with
George?
a. 19p - 27 b. 27p - 19
c. 19 - 27p d. 27 - 19p

(37) Shweta wrote an exam which had 20 questions. Each question she answers correctly gets her 10
marks. However, she loses 5 marks for each question she answers incorrectly.
She attempted all the questions and got a total of 140 marks. How many questions did she
answer wrong?
a. 8 b. 1
c. 3 d. 4

(38) Harsh deposited 900 in bank on 5th January 2003 and withdrew on 5th February 2003. Find the
interest earned by him at simple interest of 12% pa.
a. 8 b. 9
c. 10 d. 7

(39) While doing a science experiment in the physics lab, Ankur took 4 measurements of the
temperature and wrote the average of those as an answer. If the measurements of the
temperature are 2, -1, -4 and -2 then what is the final answer of his experiment?

a. 1.75 b. -1.25
c. 0.75 d. -0.25

(40) The number of schools in Thrissur is 20 less than twice the number of schools in Vadodara. If the
number of schools in Vadodara is x, how many schools are there in Thrissur?
a. 20x - 2 b. 2x + 20
c. 2x - 20 d. 20x + 2

(41) The temperature in Mumbai was 15°C in the morning which dropped to 7°C in the evening. Find
the temperature difference.
a. 4°C b. 7°C
c. 8°C d. 10°C

(42) There are 60 questions in a competitive exam. 4 marks are awarded for each correct answer,
while 1 mark is deducted for each incorrect answer. Shweta answered 42 questions correctly. If
she attempts all the questions, how many marks did she get?
a. 159 b. 158
c. 150 d. 167

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(43) The simple interest of 9600 in 3 years at 6% per annum will be same as simple interest on 5400
in 4 years at what rate?
a. 8% pa b. 9% pa
c. 10% pa d. 7% pa

(44) Priyanka has to walk, cycle, take the bus and train to get to the work. Priyanka first takes her cycle
5 29
to travel of the total distance to the bus stop. The bus takes her another of the distance.
32 128
7
Priyanka then takes a train to travel 100.125 kilometers. And finally, she walks from the
128

station to her work. What is the total distance from her house to the work?

a. 180 km b. 171 km
c. 178 km d. 187 km

(45) Gautam makes a figure which is a combination of 4 shapes. Which set of 4 shapes could he use
to make the given figure, if T stands for triangle, R for rectangle, S for square, and TZ for
trapezium?

a. T, T, T, TZ b. S, S, S, R
c. R, R, R, TZ d. T, T, T, S

ACHIEVERS SECTION

(46) The percent of the figure that is shaded is:

a. 18% b. 14%
c. 16% d. 13%

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(47) The base of the triangular field is 5 times its height. If the cost of cultivating the field at 2700 per
hectare is 546750 , find the base and the height of the field.

a. Base = 810000 m and Height = 900 m

b. Base = 4500 m and Height = 900 m

c. Base = 4500 m and Height = 810000 m

d. Base = 900 m and Height = 4500 m

(48) Lovleen's aunt lives 132 kilometers away from her house. When she wants to visit her aunt, she
1
travels of this distance by train and the rest by bus. How many kilometers does she travels by
4
bus?
a. 94 b. 35
c. 99 d. 102

(49) Find the perimeter of a park which is made of one rectangle and 2 semi-circle(s), as shown in the
figure. (All measurements are in meters, assume π = 22/7)

a. 67.68 b. 101.52
c. 84.6 d. 76.14

(50) If ∠BDC and ∠ACB are right angles, what is the measure of ∠DCB ?

a. 60° b. 35°
c. 55° d. 65°

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Answers
(1) b. 1 4 3 2

Step 1
In order to arrange the given words in the dictionary order, we have to first write the given words in the
alphabetical order.

Step 2
Compare the first letter (starting from the left most) against each other. The word whose first letter
comes earlier in the conventional alphabets, will be the first word in the list. If the 1st letters are same,
compare the 2nd letters and so on.

Step 3
Based on the above, the dictionary order of the words is:
HOWJHS, HOWJJS, HOWMHS, HOYJHS, i.e., 1 4 3 2.

Step 4
Hence, option b is the correct answer.

(2) a. Cousin

Step 1
It is given that the man playing cricket is the brother of Gita's uncle's daughter.

Step 2
Following chart shows the relation of Gita's uncle:

Step 3
Following chart shows the relation of Gita's uncle's daughter (UD):

Step 4
Following chart shows the relation of Gita's uncle's daughter's brother (UDB):

Step 5
From the above chart, we can conclude that UDB (the man playing cricket) is Gita's cousin.

Step 6
Hence, option a is the correct answer.

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(3) b. 44

Step 1
The position of Priyanka is 18th from the front, which means there are 17 people standing
before her.

Step 2
Her position is 27th from the back, which means there are 26 people standing behind her.

Step 3
So, the total number of people standing in the row is 17 (front) + 26 (back) + 1 (Priyanka) =
44.

(4) b. 19

We can count the triangles one by one with the help of the following figures. 19 triangles in
the given figure.

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(5) a. 65

Step 1
We know that the sum of each row, column and diagonal in a magic square is equal,
therefore if we add all the numbers that will fit in the given magic square and divide the sum
obtained by 3, the result will be equal to the sum of each row, column and diagonal.

Step 2
Sum of all the numbers of the given magic square = 22 + 12 + 54+

43 + 44 + 23 + 65 + 33 + 1

⟹ Sum of all the numbers of the given magic square = 297

297
⟹ Sum of each row, column and diagonal = = 99
3

Step 3
Now, the sum of each row in the given magic square is 99.
Therefore, 22 + q + 12 = 99

⟹ q + 34 = 99

⟹ q = 65

Step 4
Hence, the value of q is 65.

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(6) c. 64

Step 1
We know that the sum of each row, column and diagonal in a magic square is equal,
therefore if we add all the numbers that will fit in the given magic square and divide the sum
obtained by 3, the result will be equal to the sum of each row, column, and diagonal.

Step 2
Sum of all the numbers of the given magic square
= 32 + 27 + 59 + 70 + 38 + 43 + 48 + 16 + 54

⟹ Sum of all the numbers of the given magic square = 387

387
⟹ Sum of each row, column and diagonal = = 129
3

Step 3
By step 1, the sum of both diagonals is equal.
⟹ 32 + y + x = 59 + y + 27

⟹ 32 + x = 86

⟹ x = 86 − 32

⟹ x = 54

Step 4
Since the sum of numbers in each row is 129, therefore from 3 row and 3 column, we
rd rd

have,
⟹ 59 + q + x + 27 + c + x = 129 + 129

⟹ 86 + q + 54 + c + 54 = 258

⟹ c + q = 258 − 194

⟹ c + q = 64

Step 5
Hence, the value of c + q is 64.

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(7) d. 10:45

Step 1
Since the mirror shows the laterally inverted image of the clock, as much as the minute-hand
is to the left of 12 in the mirror image, it will be to the right of 12 by same amount of time.
Same will be the case with the hour-hand.

Step 2
Since the mirror image shows: 1:15, the actual time is 12:00 - 1:15 = 10:45, as shown below:
Mirror

(8) a. 14

Step 1
Let us observe this picture, and find the difference between consecutive numbers anti-
clockwise,
5-2=3
9-5=4
? - 9 = --
20 - ? = --
27 - 20 = 7

Step 2
We can see that the difference between consecutive terms is increasing by 1. So if this
pattern is to continue
? - 9 = 5 and 20 - ? = 6

Step 3
Above relationships hold true only when the missing number is 14. Therefore, the missing
number is 14.

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(9) a. 22

Step 1
Let us assume that in t hours, the minute hand completes t laps. In the same amount of time,
T
the hour hand completes laps.
12

Step 2
The first time the minute and hour hands overlap, the minute hand would have complete 1
lap more than the hour hand.
T
So, we get T = +1
12
12
This, implies that first overlap happen after T = hours (i.e 1:05 am).
11
Similarly, for another laps also.

Step 3
As we know that there are 24 hours in a day, so we can solve the above equation for N.
24
24 = +N
12
or, N = 24 - 2
or, N = 22

Step 4
Thus, the clock overlaps 22 times a day.

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(10) d. 14

Step 1

The first statement means that is 9 more than .

For example, their values could be:

= 1 and = 10

= 2 and = 11

= 3 and = 12

... and so on

Step 2

But it is given that is greater than 13. Therefore, the possible values are,

= 5 and = 14

= 6 and = 15

= 7 and = 16

... and so on

Step 3

But it is also given that is less than 6. Therefore, among the above possibilities, the

only possible value is,

= 5 and = 14

(11) a. 48

Step 1
If we look at the sticker groups, we notice that the total number of stickers in the animals
group = 4

Step 2
The total number of stickers in the plants group = 3

Step 3
The total number of stickers in the flowers group = 4

Step 4
Therefore, the total number of different combinations of stickers that Sarika can choose = 4 ×
3 × 4 = 48

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(12) b. 44,112

Step 1
Let us start observing from the bottom row. The difference between the consecutive numbers
is equal to 1.

Step 2
In second row from the bottom, the difference between the consecutive numbers is equal to
2.

Step 3
In the third row from the bottom, the difference between the consecutive numbers is equal to
4.

Step 4
We notice that the difference between consecutive numbers is 1 for the bottom most row,
and is doubling up as we come to the next row.

Step 5
The missing number A comes in 4th row, and since the difference between other consecutive
numbers in this row is 8, we can say that A - 36 = 8, which gives us A as 44.

Step 6
Similarly the missing number B comes in 6th row, and since the difference between other
consecutive numbers in this row is 32, we can say that 144 - B = 32, which gives us B as
112.

Step 7
Hence, A = 44 and B = 112.

(13) b. Friday

Step 1
According to the question, the number of days in the month are 30.
Number of days in a week = 7
Remainder of 30 and 7 = 2
The 2nd day of the week after Wednesday is Friday. Hence, we can say that the day on the
same date of the next month is Friday.

Step 2
Hence, option b is the correct answer.

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(14) b. ●=♦♦
Step 1
It is given that,
●●●+♦♦=♦♦♦♦♦♦♦♦
Let us take two ♦ from both sides,
●●●=♦♦♦♦♦♦
Step 2
We can rewrite the above equation as following:
3● = 6♦
Step 3
Which also means,
6
●= ♦
3

● = 2♦
● =♦ ♦
Step 4
Hence, option b is the correct answer.

(15) a. 55

Step 1
From 2nd equation, we can see that value of 3 apples is 39.
39
Therefore, value of one apple = = 13
3

Step 2
From 1st equation we can now find the value of a ice cream as follows:

= 13 - 2 = 11

Step 3
Now, we can find value of 5 ice creams:

+ + + + = 5 × 11

+ + + + = 55

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1
(16) c.
9

Step 1
Here, we have to find out the value of:
2 2 2
1 2 −2
( ) × ( ) × ( )
2 3 2

Step 2
Let us solve each term separately:
2
1 1
( ) = ,
2 4
2
2 4
( ) =
3 9

and
2
−2 4
( ) =
2 4

Step 3
2 2 2
1 2 −2
Now, ( ) × ( ) × ( ) can also be written as:
2 3 2

1 4 4
= × ×
4 9 4
1
=
9

Step 4
Hence, option c is the correct answer.

(17) b. 50°

Step 1
We know that the sum of all the interior angles of a triangle is 180°.

Step 2
Therefore, for triangle ΔABC,
∠ CBD + ∠BCA + ∠CAD = 180°
⇒ ∠CBD + 90° + 40° = 180°
⇒ ∠CBD = 180° - (40° + 90°)

⇒ ∠ CBD = 50°

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4
(18) d.
35

Step 1
2
According to the question, Sarika had covered of the total distance whereas Sita had
5
2
covered only and we are required to find the difference of the distances covered by them.
7

Step 2

The difference between the distances covered = Distance covered by Sarika − Distance
by Sarika and Sita covered by Sita
2 2
= −
5 7

14 − 10
=
35

4
=
35

Step 3
4
Hence, Sita has covered of the total distance less than Sarika.
35

(19) a. Niece

Step 1
If we look at the question carefully, we notice that Rohit is Sita's brother and Sita is Pradip's
sister.

Step 2
Or, we can say that Pradip is Rohit's brother.

Step 3
Pradip is Madhav's father and Rohit's brother.

Step 4
Or, we can say that Rohit is Madhav's uncle.

Step 5
As we do not know the gender of X, we can say that X is Rohit's nephew or niece. From the
given options, only niece satisfies all the statements.

Step 6
Hence, option a is the correct answer.

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(20) a. 109 meters

Step 1
According to the question, the distance between A and C is 91 meters and we have to find
the distance between B and D.
Let us assume the distance between B and D is x meters.

Step 2
Let us connect the point B to point D as shown in the following figure.

If we look at the figure carefully, we will notice that ΔBED is a right-angled triangle and the
distance between A and C is equal to the distance between B and E,
DE = CD - AB = 96 - 36 = 60 meters
In ΔBED,
BD2 = BE2 + DE2 (Pythagorean Theorem)
⇒ x2 = 912 + 602
By solving it, x = 109.

Step 3
Hence, the distance between B and D is 109 meters.

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(21) c. 9000

Step 1
Let us assume that the population of the town at the beginning of the first year was x.

Step 2
According to the question, the population of the town increased by 2% in the first year.
Therefore, the population of the town after the first year = x + 2% of x
2
= x + (x × )
100
100x + 2x
=
100
102x
=
100

Step 3
Next year, the population decreased by 10% and became 8262.
102x 102x
The population of the town after next year = - 10% of
100 100
Given, the population of town after next year = 8262
102x 102x 10
⇒ - × = 8262
100 100 100
102x 1020x
⇒ - = 8262
100 10000
10200x - 1020x
⇒ = 8262
10000
9180x
⇒ = 8262
10000
⇒ 9180x = 82620000
82620000
⇒ x=
9180
⇒ x = 9000

Step 4
Thus, option c is the correct answer.

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(22) d. 100.32 km

Step 1
Let us assume that r and d are the radius and diameter of the wheel, respectively, as shown
below.

Wheel

Step 2
According to the question, r = 26.6 cm
The distance traveled by truck in one rotation = 2πr
22
=2× × 26.6
7
= 167.2 cm

Step 3
The wheel makes 2000 rotation in one minute.
Therefore, the number of rotations made by the wheel in 30 minutes = 2000 × 30 = 60000
Now, the distance traveled by the truck in 30 minutes = 167.2 × 60000 = 10032000 cm
=100.32 km

Step 4
Hence, option d is the correct answer.

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(23) d. 45%

Step 1
Percentage of students who failed in History = 32%

Percentage of students who failed in General Knowledge = 39%

Percentage of students who failed in both the subjects = 16%

Step 2
Percentage of students who failed in only History = 32% - 16% = 16%

Percentage of students who failed in only General Knowledge = 39% - 16% = 23%

Total percentage of students who failed = Percentage of students who failed in only History +
Percentage of students who failed in only General Knowledge + Percentage of students who
failed in both the subjects

= 16% + 23% + 16% = 55%

Step 3
Percentage of students who passed in both the exams = 100% - Total percentage of
students who failed
= 100% - 55%,
= 45%

Step 4
Hence, 45% students passed in both the exams.

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(24) a. 38

Step 1

Let us first try to find the value of each one of , , and .

Step 2
Given, = 20
Since, the value of 5 is 20.
20
The value of will be = =4
5

Step 3
Next we are told:
= 18

We can use the above equation to find the value of .

We know =4
So, =2×4=8

We can now say,

+ 8 = 18

,or = 18 - 8 = 10

Since, the value of 5 = 10

10
The value of will be = =2
5

Step 4

Similarly calculating the values of and .

We have,
= 4 and =2

Step 5

Now, it is easy to find the value of

by substituting the value of each shape found above.

=4 +2 +2 +5
=4×4+2×2+2×4+5×2
= 16 + 4 + 8 + 10 (Remember to do all multiplications before doing additions to make sure
your answer is right!)
= 38

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(25) c. 16

Step 1
According to the question, 4 parts out of 8 are equal to 8. Here, we have to find the value of
8 parts, i.e., the complete whole.

Step 2

4
Let us draw a rectangle and divide it into 8 equal parts. As it is given that th part equals
8
to 8. So, let us shade 4 parts out of 8 and mark them as 8.
8

Step 3
Here, we get that 4 × 1 unit = 8
So, 1 unit = 8 ÷ 4
=2
Therefore, 8 × 1 unit = 8 × 2
= 16

Step 4

8
Thus, we can say that 8 units or whole or is equal to 16.
8

Step 5
Hence, option c is the correct answer.

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(26) a. 6

Step 1
The figure given below shows a triangular pyramid.
O

B C

Step 2
The triangular pyramid OABC has the following edges, namely, OA, OB, OC, AB, AC,

and BC .

Step 3
On counting the number of edges, we find that a triangular pyramid has 6 edges.

Step 4
Hence, option a is the correct answer.

(27) a. 6

Step 1
A figure has Rotational Symmetry if it still looks the same after a rotation.

Step 2

If we look at the image carefully, we notice that the given image still looks the same after 6
rotations.
Hence, the order of rotational symmetry in the given image is 6.

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17
(28) a.
9

Step 1
1
1 + can be simplified as:
1
1 +
8
1
1 +
8 + 1

8
1
= 1 +
9

8
= 1 +
9

9 + 8
=
9

17
=
9

Step 2
1 17
Therefore, the value of 1 + is .
1 9
1 +
8

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(29)

Step 1
A face is any surface that is flat.

Counting the number of faces of the cone.

Counting the number of faces of the cylinder.

Step 2

As 2 < 3, has fewer faces.

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(30) a. 2

Step 1
We have been told that the number in the center of the figure is the sum of rest of the
numbers.

Step 2
Therefore, we can write 5 + 2y + y + 3 + 2 + 3 = 19
⇒ 2y + y + 5 + 3 + 2 + 3 = 19
⇒ 3y + 13 = 19

⇒ 3y = 19 - 13

⇒ 3y = 6
6
⇒ y=
3
⇒ y=2

Step 3
Hence, option a is the correct answer.

(31) a. 20

Step 1
Let us draw a table representing the fruits' name and quantity with the help of the given bar
chart.
Fruit's name Fruit's quantity
Orange 10
Pear 60
Papaya 50
Guava 40
Pineapple 30

Step 2
From the table, we notice that the number of pears in the shop = 60
The number of guavas in the shop = 40

Step 3
Now, the difference between the number of pears and guavas in the shop = 60 - 40 = 20
Hence, we can say that there are 20 more pears than guavas.

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(32) b. −50∘ C

Step 1
We know that when anything is heated, its temperature increases and if anything is cooled,
then its the temperature decreases. If we look at the question carefully, we notice that the
temperature of the ingredient is 60∘ C.

Step 2
Since the cooling rate is 10 per hour, therefore the temperature in the freezer in 11 hours
∘
C
∘
= (−10) × 11 = −110 C

Step 3
Thus, the temperature in the freezer after 11 hours = Temperature of the ingredient +
Temperature in the freezer in 11 hours
= 60 − 110
∘
= −50 C

Step 4
Thus, option b is the correct answer.

(33) d. Friday

Step 1
According to the question, the number of days in the month are 31.
Number of days in a week = 7
Remainder of 31 and 7 = 3
The 3rd day of the week after Tuesday is Friday. Hence, we can say that the day on the
same date of the next month is Friday.

Step 2
Hence, option d is the correct answer.

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(34) b. 46x3 + 9

Step 1
Let us look at all the options one by one and find which of them will always be odd,
irrespective of x being odd or even.

Step 2
x3 + 9
Let us look at the first term x3. This term will be odd for odd values of x (for example, 33 =
27), and even for even values of x (for example, 23 = 8)

The integer 9 is an odd number. When this odd number is added to x3 which can be odd or
even, the resulting expression x3 + 9 too can be odd or even. Thus, we can say the
expression x3 + 9 will not always be odd.

Step 3
46x3 + 9
Let us look at the first term 46x3. In the first term, 46 is an even integer. Since, the product of
an even integer with any other integer is always even, we can say that the first term 46x3
must always be even.
The second term 9 is an odd integer.
Hence, we now know that the first term is even and the second term is odd. Since, we know
that the sum of an even number and an odd numbers is always odd, we can say that the
expression 46x3 + 9 must be odd.

Step 4
9x + 46
Let us look at the first term 9x. Here, 9 is an odd integer. We know that the product of an odd
integer with another odd integer can be odd or even depending upon whether the other
integer is odd or even. Thus, the term 9x can either be odd or even.

Since, 9x can either be odd or even, the expression 9x + 46 too can either be odd or even.
Thus, we can say that the expression 9x + 46 will not always be odd.

Step 5
9x
The number 9 is an odd number. When the odd number 9 is multiplied by another odd
number, the result will be an odd number. When it is multiplied by an even number, then the
result will be an even number. Thus, we can say 9x is not always odd.

Step 6
Hence, we find that the only expression that will always be odd irrespective of x being odd or
even is 46x3 + 9.

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(35) c. I only

Step 1
We know that any one side of a triangle should be less than the sum of other two sides.
Therefore, AB < AC + BC
or, AB < 14

Step 2
Also, BC < AB + AC
or, 9 < AB + 5
or, AB > 4

Step 3
Therefore, AB should be greater than 4 and less than 14.

Step 4
We find that only 6 is greater than 4 and less than 14, among the given options.
Hence, 6 is the correct answer.

(36) a. 19p - 27

Step 1
Number of boxes George had = p
Since, each box contains 19 cards, so the number of cards George had = 19p

Step 2
Number of cards given by George to his friend = 27 cards
Therefore, the cards left with George are 19p - 27.

Step 3
Hence, option a is the correct answer.

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(37) d. 4

Step 1
Total number of questions in the exam = 20

Step 2
Since, each correct answer gets 10 marks, the maximum possible marks in the exam = 20 ×
10 = 200 marks.

Step 3
Since, Shweta attempted all the questions and got a total of 140 marks, the marks lost by
her = 200 - 140 = 60 marks.

Step 4
Since, she loses 5 marks for each wrong answer and each correct answer otherwise could
get her 10 marks, the marks lost for each wrong answer = 10 + 5 = 15.

Step 5

Total marks lost

The number of questions Shweta answered wrong =
Marks lost for each wrong answer
60
=
15
=4

Step 6
Hence, Shweta got 4 answers wrong.

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(38) b. 9

Step 1
It is given that,
Principal, P = 900
Rate, R = 12%
Time, T = 5th January 2003 to 5th February 2003
= 1 months
1
= years
12

Step 2

P×R×T
Simple interest, S.I = ( )
100

1
900 × 12 ×
= 12

100
=9

Step 3
Therefore, the interest earned by Harsh is 9.

(39) b. -1.25

Step 1
According to the question, Ankur took 4 measurements of the temperature and wrote the
average of those as an answer.

Step 2
Measurements of the temperature are 2, -1, -4 and -2. So, the final answer of Ankur's
experiment = The average of 2, -1, -4 and -2
Sum of 2, -1, -4 and -2
=
Number of the measurements of the temperature
-5
=
4
= -1.25

Step 3
Hence, option b is the correct answer.

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(40) c. 2x - 20

Step 1
It is given that the number of schools in Vadodara = x
So, twice the number of schools in Vadodara = 2x

Step 2
20 less than twice the number of schools in Vadodara = 2x - 20
Hence, the number of schools in Thrissur = 2x - 20

Step 3
Hence, option c is the correct answer.

(41) c. 8°C

Step 1
We know,
The temperature in the morning = 15°C

The temperature in the evening = 7°C

Also, the temperature difference = Higher Temperature − Lower Temperature

= 15°C − 7°C
= 8°C

Step 2
Hence, the temperature difference is 8°C.

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(42) c. 150

Step 1
Total number of questions in the competitive exam = 60
Marks awarded for each correct answer = 4
Marks deducted for each incorrect answer = 1

Step 2
Since, Shweta answered 42 questions correctly, total marks obtained by Shweta
= 4 × 42
= 168

Step 3
So, the number of incorrect answers = Total number of questions in the exam - Number of
correct answers
= 60 - 42
= 18

Step 4
Thus, the total marks obtained by Shweta in the exam = Total marks for correct answers -
Total marks deducted for incorrect answers
= 168 - ( 1 × 18)
= 168 - 18
= 150

Step 5
Hence, option c is the correct answer.

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(43) a. 8% pa

Step 1
Let's first find the simple interest on 9600 at rate of 6% per annum. for 3 years.
Principal, P = 9600
Rate, R = 6%
Time, T = 3 years
Simple interest, S.I.
P×R×T
=( )
100
9600 × 6 × 3
=
100

Step 2
Now, we have to find the rate per annum by using the above simple interest.
Let the rate be R per annum.
Principal, P = 5400
Time, T = 4 years
Simple interest, S.I.
P×R×T
=( )
100
5400 × R × 4
=
100

Step 3
It is given that both interests are same. Therefore,
5400 × R × 4 9600 × 6 × 3
=
100 100
9600 × 6 × 3
⇒ R=
5400 × 4
⇒ R = 8%

Step 4
Therefore, the rate required for the same simple interest will be 8% per annum.

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(44) c. 178 km

Step 1
Given, Distance covered by train = 100.125 km
To find the total distance from Priyanka's house to her work, first, we will calculate the
fraction of the distance she covered by train.

Step 2
The fraction of the distance covered by train = 1− ( Distance covered by cycle + Distance
covered by bus + Distance covered by walking)
5 29 7
The fraction of the distance covered by train = 1 − ( + + )
32 128 128

7
= 1 −
16

9
=
16

Step 3
Now,
9
Distance covered by train = of the total distance
16
16
The total distance = 100.125 × = 178 km
9

Hence, the total distance from her house to the work is 178 km.

(45) a. T, T, T, TZ

If we look at the figure, we notice that it is combination of 3 triangles and one trapezium.
Therefore, T, T, T, TZ is the correct answer.

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(46) b. 14%

Step 1
If we count the shaded squares and half-squares in the given figure, we will notice that
the total number of shaded squares are 3.5(count two half-squares as one small square).

Step 2
Also, total number of squares = 25

Shaded part 3.5

As we know fraction of shaded part = =
Whole Part 25

Step 3
Converting the proper fraction into percentage, we have:
3.5
× 100% = 3.5 × 4% = 14%
25

Step 4
Thus, we see that 14% of the figure is shaded.

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(47) b. Base = 4500 m and Height = 900 m

Step 1
Total cost of cultivating the field = 546750

Rate of cultivating the field = 2700 per hectare

Total cost
Area of the field = ( )hectares
Cost per hectare

546750
= ( ) hectares
2700

= 202.5 hectare

2
= 202.5 × 10000 m
2
= 2025000 m

Step 2
Let the height of the field be x m .
Then, its base = 5x m

1
Area of the triangular field = × Base × Height
2
1
2
⟹ 2025000 m = × 5x × x
2

1
2
⟹ 2025000 = × 5x
2

2 × 2025000
2
⟹ = x
5
2
⟹ 810000 = x

⟹ 900 m = x

So,
Height of the field = 900 m
Base of the field = 5 × 900 = 4500 m

Step 3
Thus, the height of the field is 900 m and the base of the field is 4500 m.

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(48) c. 99

Step 1
The total distance between Lovleen's house and her aunt's house = 132 km

Step 2

1
: The distance Lovleen travels by train = of 132 km
4
1
= × 132 km
4
= 33 km

Step 3
In order to find the distance travelled by bus, let us subtract the total distance and the
distance she traveled by train = 132 - 33 = 99

Step 4
Therefore, Lovleen traveled 99 km by bus to reach her aunt's house.

(49) c. 84.6

Step 1

In the given figure, we can clearly say that the perimeter of the park = The length of the sides
(which do not contains semi-circle) of the rectangle + The perimeter of the semi-circles.
22 16.1 22 16.8
= 16.1 + 16.8 + ( × )+( × ) ...(Perimeter of the semi-circle is π(d/2),
7 2 7 2
where d is the diameter)
= 16.1 + 16.8 + 25.3 + 26.4
= 84.6 meters

Step 2
Hence, option c is the correct answer.

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(50) c. 55°

Step 1
We know that the sum of all the interior angles of a triangle is 180°.

Step 2
Therefore, for triangle ΔABC,
∠ CBD + ∠BCA + ∠CAD = 180°
⇒ ∠CBD + 90° + 55° = 180°

⇒ ∠ CBD = 180° - (55° + 90°)

⇒ ∠ CBD = 35°

Step 3
Similarly, for the triangle ΔCDB,
∠ CBD + ∠DCB + ∠CDB = 180°
⇒ 35° + ∠DCB + 90° = 180°
⇒ ∠DCB = 180° - (35° + 90°)

⇒ ∠ DCB = 55°

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