Data Sufficiency

Anatomy of a Data Sufficiency question:

While the genre of Data Sufficiency is unique, the structure is not – all Data
Sufficiency questions are structured exactly the same, with three key elements:

Consider this example to see what a Data Sufficiency question will look like:

QUESTION STEM
By what percent was the price of a certain candy bar increased?

STATEMENTS
The price of the candy bar was increased by 5 cents.
The price of the candy bar after the increase was 45 cents
ANSWER CHOICES:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
EACH statement ALONE is sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement
ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

If you’re relatively new to Data Sufficiency, the most striking feature of this
question is likely the answer choices – they’re not numbers that might answer
the questions, they’re more logical descriptions of when you might be able to
answer the question.

In this you just need to check that are we able to reach out to an answer.
From both the statements answer might be different.
Data Sufficiency Decision Tree:
Assess each statement to determine whether it is sufficient or not, and this tree
will lead you to the correct answer:
PRACTICE QUESTIONS:
Each problem consists of a question and two statements, labeled (I) and (II), in
which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question.
Mark,
A. If statement (i) ALONE is sufficient, but statement (ii) alone is not sufficient
to answer the question asked.
B. If statement (ii) ALONE is sufficient, but statement (i) alone is not sufficient
to answer the question asked.
C. If EACH statement ALONE is sufficient to answer the questions asked.
D. If BOTH statements (i) and (ii) TOGETHER are sufficient to answer the
question asked, but NEITHER statement ALONE is sufficient
E. If statements (i) and (ii) TOGETHER are NOT sufficient to answer the
question asked and additional data specific to the problem are needed.
1. Five persons are to be seated in a round table conference, who will be
seated between Ram and Gita?
I. Ram will sit on the right of Vinay and on the left of Kamal.
II. There will be two persons seated between Vinay and Kamal.

2. When is the next bus scheduled for Mumbai from Delhi?

I. Every 30 minutes a bus is scheduled for Mumbai from Delhi. The return
bus leaves Mumbai for Delhi every 45 minutes.
II. It is 4.45pm now .15 minutes ago one bus has left for Mumbai as per the
schedule whereas the bus from Mumbai has arrived about 30minutes ago

3. Among four friends P,Q,R and S, who has scored the highest runs in the
cricket match?
I. P took more wickets than S but scored less runs than R.
II. Q scored more runs than P but took less wickets than S and R.
4. Among five friends P,Q,R,S and T, who ranks 3rd in terms of salary obtained
by them?
I. T’s salary is more than P and Q but not more than S.
II. R’s salary is the lowest among them.

5. How long does it take to reach city Y from city X?

I. Sangeeta was scheduled to leave the city X at 17.15 hours but got late by
45minutes and reached city Y at 16.15 hours the next day.
II. Sangeeta reached the bus stand of city X at 14.25 hours and got the bus
after waiting for 35 minutes. She reached city Y at 3.15 hours the next day.

6. Among P, K, D and R, who could be the son of M?

I. P and K are sisters
II. D is the mother of K and wife of M.
7. Who among N, F, P, J and D is youngest?
I. P and J are younger than N and D.
II. F is younger than N, D and P but older than J.

8. Who among T, R and S is to the East of P?

I. R, who is to the West of P, is not as near to S as P, S is in the farthest East.
II. P is not as far away from S and T

9. What is K’s rank from the bottom in a class of thirty students?

I. M’s position is 3rd from the top and there are five students between M and K.
II. P’s position is 4th from the bottom and there are 7 students between P and K.
10. Who is to the immediate right of Mohan when Mohan, Salil, Bhusan, Suresh
and Jayesh are sitting around a circle facing at the centre?
I.Salil is 3rd to the left of Mohan.
II. Bhusan is between Salil and Jayesh.

11. What is the rate of interest p.a on an amount of Rs. 12000 deposited in a
bank?
I. The difference between the simple interest and the compound interest is Rs
172.8.
II. The simple interest for two years is Rs. 2880.

12. What is the profit earned by selling the laptop for Rs 26,250?
I. The cost price of five such laptops is equal to selling price of 4 such laptops.
II. 25% of the profit is earned by selling each laptop.
13. How many women can complete a piece of work in 15 days?
I. If 12 women can complete the same piece of work in 20 days.
II. If 10 men can complete the same piece of work in 12 days.

14. What is the three digit number?

I. The three digit number is an exact multiple of 13.
II. The first and the third digit are 7.

15. What is the age of C in a group of A, B, C, D and E whose average is 45 years?

I. Average of the ages of A and B is 53.
II. Average of the ages of D and E is 47.
16. In a library 10% of the books are added every year, what was the number
of books that the library had in 1994?
I. During 1996, 10,000 books were added
II. During 1995, the library had 1,00,000 books

17. What is the difference in the ages of P and K?

I. P is 20 years older than M
II. M is 2 years younger than Z

18. D is the sister of C. how is D related to A?

I. A is the sister of B
II. B is the brother of C

19. A, B,C,D and E are sitting in a row. What is the position of B from the left end?
I. A is sitting at one end second right of D who is the immediate neighbor of C and B
II. E is to the left of B
20. How INDIA will be coded?
I. If ALIVE is coded as LAIEV
II. If JAPAN is coded as AJPNA

21. What will come in place of c in the series a,b,c,d,e?

I. a,b,c,d,e are five consecutive even numbers
II. common difference between two consecutive numbers is 2 and a is the
second smallest natural number

22. Who among A,B,C,D and E is the smallest?

I. B is taller than E and D is taller than A but smaller than E.
II. D is not the tallest and C is not the smallest
23. X borrowed Rs. 1000 from Y on SI. What is the rate per annum?
I. After 4yrs, X paid Rs. 100 as interest.
II. After 4yrs, X paid Rs. 1100 to settle the loan.

24. What is the total salary of Mr. X and his wife at present?
I. Salary of X and his wife together is 20% more than what they earned last month.
II. Last month salary of X was Rs. 600 more than that of his wife.

25. A figure is composed of ten 1- inch cubes. What is the weight?

I. The cubes are arranged in five rows to two each.
II. The cubes have an average weight of 1 ounce each.
26. Is the average age of the students of a school less than 17 years?
Statement I : The strength of the class VIII is less than 25% of the strength of
the school.
Statement II : The average age of the students of class VIII of the school is 18
years and that of the remaining classes is 16 years.

27. Among 20 retired persons, is the number of persons, who are having at
least 20 years of service, less than 8?
Statement I : Exactly 17 persons joined the service before 2000 and exactly 14
persons retired after 2020.
Statement II : Exactly 14 persons joined the service after 2000 and exactly 6
persons retired before 2020.

28. The lengths of trains A and B are in the ratio 2:3. Which of them takes less
time to cross the same platform?
Statement I : The time taken by train A to cross train B when they are moving
in opposite directions is half the time taken by it to cross train B, when moving
in the same direction.
Statement II : The ratio of the length of train B to that of the platform is 4 : 3.
Q. No. Answer Q. No. Answer Q. No. Answer Q. No. Answer Q. No. Answer

1 E 2 D 3 E 4 E 5 C

6 D 7 B 8 A 9 C 10 D

11 B 12 C 13 A 14 D 15 D

16 C 17 E 18 D 19 E 20 C

21 E 22 D 23 C 24 E 25 B

26 D 27 E 28 E
Data Interpretation
Data Interpretation is one of the easy sections of one day competitive Examinations. It is
an extension of Mathematical skill and accuracy. Data interpretation is nothing but drawing
conclusions and inferences from a comprehensive data presented numerically in tabular
form by means of an illustration, viz. Graphs, Pie Chart etc. Thus the act of organizing and
interpreting data to get meaningful information is Data Interpretation.

SOME USEFUL TIPS :

1 . Data Interpretation questions are based on information given in tables and graphs.
These questions test your ability to interpret the information presented and to select the
appropriate data for answering a question.
2 . Get a general picture of the information before reading the question. Read the given
titles carefully and try to understand its nature.
3 . Avoid lengthy calculations generally, data interpretation questions do not require to do
extensive calculations and computations. Most questions simply require reading the data
correctly and carefully and putting them to use directly with common sense.
4 . Breakdown lengthy questions into smaller parts and eliminate impossible choices.
5 . Use only the information given and your knowledge of everyday facts, such as the
number of hours in a day, to answer the questions based on tables and graphs.
6 . Answer the questions asked and not what you think the questions should be.
7 . Be careful while dealing with units.
8 . To make reading easier and to avoid errors observe graphs keeping them
straight.
9 . Be prepared to apply basic mathematical rules, principles and formulae. 10. Since
one of the major benefits of graphs and tables is that they present data in a form that
enables you to readily make comparisons, use this visual attribute of graphs and
tables to help you answer the questions. Where possible, use your eyes instead of
your computational skills.
TABLES
• Tables are often used in reports, magazines and newspaper to present a set of
numerical facts. They enable the reader to make comparisons and to draw quick
conclusions. It is one of the easiest and most accurate ways of presenting data.
They require much closer reading than graphs of charts and hence are difficult
and time consuming to interpret. One of the main purposes of tables is to make
complicated information easier to understand. The advantage of presenting data
in a table is that one can see the information at a glance. While answering
questions based on tables, carefully read the table title and the column headings.
The title of the table gives you a general idea of the type and often the purpose
of the information presented. The column headings tell you the specific kind of
information given in that column. Both the table title and the column headings are
usually very straight forward.
GRAPHS
There may be four types of graphs:
1) Circle Graphs: Circle graphs are used to show how various sectors are in the
whole. Circle graphs are sometimes called Pie Charts. Circle graphs usually give the
percent that each sector receives In such representation the total quantity in question
is distributed over a total angle of 360°. While using circle graphs to find ratios of
various sectors, don't find the amounts each sector received and then the ratio of the
amounts. Find the ratio of the percentages, which is much quicker.

2)Line Graphs: Line graphs are used to show how a quantity changes continuously. If
the line goes up, the quantity is increasing; if the line goes down, the quantity is
decreasing; if the line is horizontal, the quantity is not changing.

3) Bar Graphs: Given quantities can be compared by the height or length of a bar
graph. A bar graph can have either vertical or horizontal bars. You can compare
different quantities or the same quantity at different times. In bar graph the data is
discrete. Presentation of data in this form makes evaluation of parameters
comparatively very easy.
4) Cumulative Graphs : You can compare several categories by a graph of the
cumulative type. These are usually bar or line graphs where the height of the bar or
line is divided up proportionally among different quantities.

CONCEPT TO REVISE:
Average = Sum of observations/Total number of observations

Percentage Increase = (Increase/Original Value)*100

Percentage Decrease = (Decrease/Original Value)*100

where, Original Value is the value to which increase and decrease has been done
or the old value
Example 1: The table below reports annual statistics related to rice production
in selected states of India for a particular year:
Which two states account for the highest productivity of rice (tons produced per
hectare of rice cultivation)?
(1)Haryana and Punjab
(2)Punjab and Andhra Pradesh
(3)Andhra Pradesh and Haryana
(4)Uttar Pradesh and Haryana

How many states have a per capita production of rice (defined as total rice production
divided by its population) greater than Gujarat?
(1)3
(2)4
(3)5
(4)6
An intensive rice producing state is defined as one whose annual rice production
per million of population is at least 400,000 tons. How many states are intensive
rice producing states?(approx)
(1)5
(2)6
(3)7
(4)8
Study the following table and answer the questions given below it.
Production of sugar by six major production units of India in Million Tonnes
In which month the unit B has a contribution of approximately 15% in the total
sugar production?
a) August
b) June
c) July
d) April

Which of the following units shows continuous increase in production of sugar

over months?
a)A
b)B
c)C
d)D
In the case of Unit E, in which of the following pairs of months the production of sugar
was equal?
a) April & June
b) June & July
c) July & August
d) April & May

In the month of June, how many units have a share of more than 25% of the total
production of sugar?
a)one
b)Three
c)Two
d)Four
What was approximate percentage decrease in sugar production of unit B in June
as compared to April?
a)8 %
b)10%
c)15%
d)18%
The table below gives the production capacity (in thousands units) and the percent
utilisation in respect of three products (A,B and C) over five years for an organisation.
Study the table carefully and answer the questions that follow.
Approximately, what was the overall utilization for all products taken together for
the year 1993?
a)50%
b)55%
c)60%
d)65%

What is the approximate overall growth rate in respect of total capacity for the
period shown?
a)5 %
b)10%
c)15%
d)20%
In which of the following years was the production of product A the maximum for
all period shown?
a)1993
b)1997
c)1996
d)1994

What is the average production of product B over the period shown?

a)21,600
b)24,200
c)34,600
d)28,800
In which of the following years was the production of product C the minimum for the
period shown?
a)1997
b)1994
c)1993
d)1996
PIE CHART (CIRCULAR
GRAPH)
The pie-chart drawn below shows the spending of a country on various sports
during a particular year. Study the pie-chart carefully and answer the questions
given below it.
PERCENT OF MONEY SPENT ON VARIOUS SPORTS FOR ONE YEAR
If the total amount spent on sports during the year was Rs. 15000000, the amount spent on cricket and hockey together was
a)Rs. 2500000
b)Rs. 3750000
c)Rs. 5000000
d)Rs. 6000000

Out of the following, the country spent the same amount on

a)Hockey and Tennis
b)Golf and foot ball
c)Cricket and Foot ball
d)Football and Hockey

Pie-chart shows that the most popular game of the country is (on the basis of money spent)
a)Cricket
b)Foot ball
c)Basket ball
d)Hockey
The ratio of the total amount spent on football to that spent on hockey is
a) 1: 15
b) 1: 1
c)15:1
d)3: 20

If the total amount spent on sports during the year was Rs. 12000000, how much
was spent on basket ball?
a)Rs. 950000
b)Rs. 1000000
c)Rs. 1200000
d)Rs. 1500000
The pie chart given below shows the expenditure incurred in bringing out a
book, by a publisher.
What is the central angle showing the cost of paper?
a)16°
b)32 °
c)28.8 °
d)57.6°

If the cost of printing is Rs. 23400, the royalty is:

a)Rs. 6500
b)Rs. 2340
c)Rs. 4680
d)Rs. 7840
If miscellaneous expenditures amount to Rs. 18000, the expenditure on canvassing will
be:
a)Rs. 8000
b)Rs. 14400
c)Rs. 46800
d)Rs. 40500

Royalty on the book is less than canvassing expenditure by:

a)8 %
b)80%
c)44 (4/9)%
d)None
BAR GRAPH
Study the following graph and answer the questions given below it.
PRODUCTIONS OVER MONTHS
Which of the following months shows maximum increase in the production over its
immediately preceding month?
(a)March
(b)April
(c)May
(d)June

By how much is the average production of the last five months more than the average
production of the first three months? (Approx.)
(a)740
(b)700
(c)720
(d)660
Which month exactly shows the same increase in production over its immediately
preceding month as the month of march shows over that of February?
(a)February
(b)April
(c)May
(d)None of these

Approximately by what percentage did the total production in the two consecutive
months of July and August increase over the total production in the first two
consecutive months of January and February?
(a)95
(b)75
(c)65
(d)55
How many months have more than the average production for the 8 months period?
a)5
b)2
c)3
d)4
LINE GRAPH
Study the following graph carefully and answer the questions given below:
Production of three types of vehicles by a company over the years (in thousand)
What was the percentage increase in the production of C type vehicles from 1985
to1986?
a)10
b)5
c)20
d)None of these

The number of A type vehicles produced in 1986 was what percent of the number of
C type vehicles produced in 1988?
a)33 1/3
b)66 2/3
c)50
d)15
In how many years was the production of A type vehicles less than its average
production over the given years?
a)2
b)4
c)3
d)1

What was average number of B type vehicles produced by the company over the years?
a)20,000
b)25,000
c)15,000
d)30,000
Study the following graph carefully and answer the questions given below it. Income
and Expenditure of a Company over the years (Rs. in crore)
In which of the following years was the difference between the income and the
expenditure the maximum?
a) 1988
b) 1991
c) 1986
d) 1987

The income in 1987 was equal to the expenditure in which of the following years?
a) 1985 only
b) 1990 only
c) 1985, 1989 and 1991
d) 1988 and 1989
What was the approximate percentage drop in expenditure from 1988 to 1989?
a)35
b)25
c)75
d)40

What was the percentage increase in income from 1987 to 1988?

a)175
b)75
c)60
d)125

In how many of the given years was the expenditure more than the income?
a)1
b)3
c)4
d)2
Study the following pie-chart and the table and answer the questions based on them.
If the population of village R in 1997 is 32000, then what will be the population of village
Y below poverty line in that year?
a)14100
b)15600
c)16500
d)17000

The ratio of population of village T below poverty line to that of village Z below poverty
line in 1997 is:
a)11 : 23
b)13 : 11
c)23 : 11
d)11 : 13
Find the population of village S if the population of village X below poverty line in 1997 is
12160.
a)18500
b)20500
c)22000
d)26000

If in 1998, the population of villages Y and V increase by 10% each and the percentage
of population below poverty line remains unchanged for all the villages, then find the
population of village V below poverty line in 1998, given that the population of village Y in
1997 was 30000.
a)11250
b)12760
c)13140
d)13780
Answer Q. No. Answer Q. No. Answer Q. No. Answer Q. No. Answer

1 2 2 3 4 4 C 5 A

D 7 A 8 B 9 A 10 D

B 12 A 13 C 14 D 15 D

A 17 B 18 D 19 D 20 A

D 22 C 23 D 24 D 25 D

D 27 D 28 D 29 C 30 B

A 32 B 33 C 34 B 35 B

D 37 B 38 C 39 C 40 B