 # CAT Data Sufficiency Questions with Answers

#### Data Sufficiency

Data sufficiency questions are tricky and require thorough understanding of the topic involved to solve. The following data sufficiency practice questions with solutions will be helpful in understanding the approach that one must adopt to solve data sufficiency questions.

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Instructions

For the following questions answer them individually

Question 1

How long would one man, one woman and one child take to build a given building?
Statement 1: One man, 5 women and 9 children would take 52 days to build the same building
Statement 2: Four men, 8 women and 12 children would take 28 days to build the same building.

Question 2

The average age of a family of five is A. Find A?
Statement 1: The ages are in a geometric progression and the product of the ages is 1048576
Statement 2: The ages of the family are roots of the equation $$x^5 - 50x^4 + ax^3 + bx^2 + 44064x - 80640 = 0$$

Question 3

What is the value of X*Y?
Statement 1: HCF of X and Y is 3
Statement 2: LCM of X and Y is 36

Question 4

Given that the ages of A and B are integers greater than 20 and less than 70. What are their individual ages?
Statement 1: A is a perfect square and B is a perfect cube.
Statement 2: A and B are twins

Question 5

Priya went to a candy shop to buy some caramel pops, toffee bites and mango pops. What is the total price of one caramel pop, one mango pop and one toffee bite?
Statement 1: The cost of three caramel pops, five toffee bites and seven mango pops is Rs 68
Statement 2: The cost of two caramel pops, three toffee bites and four mango pops is Rs 41

Question 6

A card is randomly drawn from a standard pack of 52 cards without replacement. Is the card a face card?
Statement 1: The probability of drawing two Tens from the remaining 51 cards is 1/425
Statement 2: The probability of drawing two Queens from the remaining 51 cards is 2/425

Question 7

If X and Y are two natural numbers, such that X>Y, find X-Y

Statement 1: HCF(X,Y) = 36
Statement 2: X+Y = 288

Question 8

Given that x and y are integers, if $$\sqrt{x^{3}-x^{2}-y} = 7$$ what is the value of x?
Statement 1: $$x^{2}-x=12$$
Statement 2: $$y^{2}-y=2$$

Question 9

Find X?
Statement 1: X is a three digit perfect square with the same hundreds and tens digit
Statement 2: X is an odd number

Question 10

Given that X is an odd natural such that such that $$2^{80} > X^{40}$$ ,find X?
Statement 1: X is a prime
Statement 2: $$X^{20} > 2^{30}$$