# Level 3- Data Sufficiency Practice Quiz 1- Hard

### DIRECTIONS for following questions 1 to 10: You have to decide whether the data given in the statements is sufficient to answer the question or draw the conclusion of the statement in the question.

Mark 1 if statement A alone is sufficient but B alone is not sufficient
Mark 2 if statement B alone is sufficient but statement A alone is not sufficient
Mark 3 if both the statements A and B are needed
Mark 4 if each of statement A or statement B alone is sufficient.
Mark 5 if both of them together are not sufficient

What could be the maximum number of people in a group reading both newspapers X & Y?
A 50% of persons of the group read newspaper X.
B 30% of persons of the group read newspaper Y.

Statement (A) “50% of persons read newspaper X”, is not sufficient since we can’t conclude anything.
Statement (B) “30% of persons read newspaper Y”, is not sufficient since we can’t conclude anything.
But using both together,
We can say maximum 30% of persons could read both newspaper X & Y.
So it is seen that (A) and (B) together are sufficient to answer the question.

2. A shopkeeper sells a phone X on 20% profit. What is the Cost Price of phone X?
A Average of all the phones sold by shopkeeper is 225.
B Selling Price of Phone X is Rs. 14400.

Given that, Profit = 20%
SP= 120% of CP
Statement (A) is not sufficient since it implies only that average of all the phones sold by shopkeeper is 225. Therefore, we can’t conclude the answer.
From the second statement, SP=Rs. 14400
SP= 120% of CP
14400= 120% of CP
CP= Rs. 12000
Hence, Statement B alone is sufficient to answer the question.

3. How many maximum milliliters of water can a tank hold?
A The tank currently holds 200 milliliters of water
B If 150 milliliters of water is added to the tank then tank is half filled.

Statement A alone is not sufficient since it implies only that tank holds at least 200 milliliters. Therefore, we can’t conclude the answer.
Statement B alone is not sufficient because it does not mention the current status of water in the tank.
By combining both the statements,we can say
if t is the capacity of the tank and on adding 150 mls of water, then the volume of water will be 350 milliliters which is equal to 1/2 of capacity of tank
i.e t/2= 350 milliliters.
t=700 milliliters.
So, we can find out capacity of the tank. Hence, option 3.

4. Product of X and Y is 48 where X & Y are positive integers. Find X.
A Y/12 is an integer.
B X/4 is an integer.

From the first statement, Y can be 12, 24 or 48.
From the second statement, X can be 4, 8,12,16,20,….,48.
But if we combine both the statements, we can say Y = 12,X = 4
So,both the statements A and B are needed. Hence, answer is option 3

5. ls xy > 5?
A 1 ≤ x ≤ 3 and 2 ≤ y ≤ 4.
B x + y = 5

Statement A alone is not sufficient, since the product could be as small as (1)(2) = 2 or as large as (3)(4) = 12 Therefore, the answer must be 2, 3, or 5.
Statement B alone is not sufficient since if x were 1, y would be 4 and xy = 4; but if x were 2, y would be 3 and xy = 6. Hence, the answer must be 3 or 5.
Both statements together are not sufficient since both of the examples x = 1, y = 4 and x = 2, y = 3 are consistent with both statements. Therefore, the best answer is 5.

6. For integers x and y, x2 + xy +24x = 81 , what is the value of x?
A x+y=3
B x2+y=5

From statement A,
We have x+y = 3. When we substitute back into the main equation,
x2 + xy +24x = 81
x( x + y ) + 24x = 81
3x + 24x = 81
27x=81; we get x =3 which is integer. Statement A alone is sufficient to get the answer.
From statement B,
x2 = 5-y
So, equation becomes, 5 – y + xy + 24 x = 81
xy – y + 24x = 76
y ( x – 1 ) + 24 ( x – 1 ) = 76 – 24 = 52
( y + 24 ) (x – 1 ) = 52 = 1 x 52, 2 x 26, so on.
Hence Statement B alone is not sufficient to answer the question.
Statement A alone is sufficient to get the answer. Hence, answer is option 1.