This document provides guidance on data sufficiency problems. It explains that there are two types of data sufficiency problems - those requiring a yes/no answer and those requiring a numerical solution. It provides examples of each type and explains how to determine if statement I alone, statement II alone, or both statements together are sufficient to answer the question. It emphasizes that the goal is to determine sufficiency, not to solve the problem. It also contains examples of data sufficiency questions and explains the reasoning to determine if statements I and/or II provide sufficient data to answer each question.

1. DATA SUFFICIENCY

2. DATA SUFFICIENCY

3. DATA SUFFICIENCY

4. DATA SUFFICIENCY

5. DATA SUFFICIENCY

6. DATA SUFFICIENCY

7. • If you find the statement (i) alone is sufficient to answer
the question do not blindly put down
• A and go on to the next problem. Look at statement (2)
alone also. If (2) also is sufficient, the
• answer is “D”.
• The Data Sufficiency questions usually have two types of
solutions. One, in which you are
• required to determine only yes or no as the answer, and
other, in which a numerical solution
• is required. For example,

8. • Solution Type I
• The Data Sufficiency questions which require only a „yes‟ or „no‟ as the answer may appear
• like:
• Ø Is Binny taller than Sammy?
• Ø Is Manu paying more than she should?
• Ø Is x > 0?
• Ø Is interest paid to the bank in 5 years more than rs.6000?
• Solution Type II
• The Data Sufficiency questions which require an actual numerical solution may sound like:
• Ø How tall is Binny?
• Ø How much Manu is paying to her house-maid?
• Ø Determine the value of x?
• Ø Calculate the interest earned by the bank on a loan of rs.10000 @ 5% per annum for a
• term of 2 years?
• REMEMBER YOU SHOULD NOT SOLVE THESE PROBLEMS. JUST CHECK
• WHETHER THE GIVEN DATA IS SUFFICIENT TO SOLVE THESE PROBLEMS.
• You should review the basic concepts of highschool algebra and plane geometry (upto +2
• level). You need not have advanced mathematics background.

9. • Examples:
• How much change does Mahesh receive
from a `.5 note?
• (i) Mahesh buys a total of 6 oranges at 50
paise each. .
• (ii) Mahesh receives more than `.3 in
change.

10. • Look at (I). If Mahesh buys a total of 6 oranges at
50 paise each, it is easy to find how much money
Mahesh spends. There is no need to multiply 6
and 50 paise. We can easily find the change
from rs.5 note.
• Statement (II) does not tell us anything definite so
it cannot be used to answer the question.
• Thus Choice A is correct.

11. • How many people are there at the party?
• (i) The party has between 20 and 30 people.
• (ii) The number of the people at the party is
a prime number between 24 and 30.
(A prime number cannot be divisible by
another number except one and the same
number).

12. • Certainly statement (I) alone cannot answer
the question. Now look at statement (II).
• The only prime number between 24 and 30
is 29.
• Thus statement (II) alone is sufficient to
answer the question.
• Thus Choice B is correct.

13. • Is x + y positive?
• (i) x3 = 20 y
• (ii) y3 = -129

14. • Look at statement (I).
• This does not tell us anything about x + y.
• Now, look at the second statement (II).
• This tells us that y is negative (since y3 is
negative).
• But this does not answer our question.
• However if y is negative according to statement
(II), then according to statement (I) x is also
negative. Therefore x + y must be negative

17. • The first statement implies that y2 > 38
• So statement (I) implies that y2 > 38.and we have
answered the question.
• Now look at the statement (II).
• If y = 7, then y2=49 and certainly 49 > 37.
• Thus statement (II) answers our question. Since
both the statements (I) and (II) answer our
question by themselves, choice D is correct

18. • What is the perimeter of the triangle ABC?
• (i) Triangle ABC is a right triangle.
• (ii) The area of triangle ABC = 30.

19. • Statement (I) alone certainly does not answer our
question because the fact that a triangle is a right
triangle. Statement (II) tells us that the area is 30.
• Statement (2) alone will not tell us what the
perimeter of the triangle is.Suppose we look at the
statements (I) and (II) together.
• Let the sides of the right triangle be x , y ,z. where
z is the hypotenuse. The area of the triangle is ½
xy = 30
• We cannot determine the perimeter. So,Choice E
is correct.

20. • The ratio of the prices of three different
types of cars is 3:2:5. Find the price of the
car of medium price.
• A) The difference between the costliest and
the cheapest cars is `.30,000.
• B) The Cheapest car costs `.20,000.
• Ans: C

21. DS – Ages
• Find the age of Amar‟s Wife
• A. Amar told Bhavan, “My wife is 24 years
older than your daughter. Your wife is 6
years older than my son.”
• B. Bhavan told Amar, “ Your wife is as
much older than my wife as 7 times the age
of my daughter is more than your son‟s age.
• Sol: 4 Amar Bhavan
Wife y + 24 x
Son x – 6 y
Given 7y – (x) = (y+24) – (x–6)

22. DS - from CTS
• How many visitors saw the exhibition
yesterday?
• I. Each entry pass holder can take up to
three persons with him / her.
• II. In all, 243 passes were sold yesterday.
• Ans: E

23. • How much was the total sale of the
company?
• I. The company sold 8000 units of product
A each costing Rs. 25.
• II. The company has no other product line
• Ans: D

24. • In what proportion would Raj, Karan and
Altaf distribute profit among them
• I. Raj gets two-fifth of the profit.
• II. Karan and Althaf have made 75% of the
total investment.
• Ans: E

25. • What time did the train leave today.
• I. The train normally leaves on time
• II. The scheduled departure is at 14.30.
• Ans: E.

26. • On which day in January, Subhas left for
Germany?
• I. Subhas has so far spent 10 years in
Germany.
• II. Subhas friend Anil left for Germany on
15th February and joined Subhas 20 days
after Subhas arrival.
• Ans: B.

27. TYPE II
• In each question, information concerning one or both of
the quantities to be compared is given in the item column.
• Directions: For each of the following questions, two
quantities are given – one in column A and one in column
B. Compare the two quantities and mark your answer sheet
with the correct conclusion.
• Mark A if the quantity in column A is greater.
• Mark B if the quantity in column B is greater
• Mark C if the two quantities are equal.
• Mark D if the relationship cannot be determined from the
information given.