Integers Actual Questions in XAT 2023

Q1. Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

1. 67
2. 58
3. 49
4. 40
5. None of the above

EXPLANATION

r and s are positive integers. For their difference to be as large as possible. r and s should be as far apart as possible.
r = 1; s = 59
The max difference between r and s is 59 – 1 = 58.

Q2. Let x and y be two positive integers and p be a prime number. If x (x – p) – y (y + p) = 7p, what will be the minimum value of x – y?

1. 1
2. 3
3. 5
4. 7
5. None of the above

EXPLANATION

For x and y to be integers, s and d should both be even or should both be odd.