data sufficiency

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.