IBPS PO Quantitative Aptitude: Number Theory questions with solutions

Q1. Set A contains 3 consecutive prime numbers while set B contains 2 consecutive odd numbers. Sum of largest number of set A and set B is 64 while largest number of set A is 4 less than the 3 times of largest number of set B. Find the smallest number of set A.

1. 47
2. 41
3. 53
4. 43

Answer: 41

Let largest of A = a, largest of B = b. Eq1: a + b = 64. Eq2: a = 3b - 4. Substituting: (3b-4) + b = 64 → 4b = 68 → b = 17. So a = 64-17 = 47. Set B = {15, 17} (consecutive odd). Set A = 3 consecutive primes ending at 47: primes are 41, 43, 47. Smallest = 41.

Q2. Two-digit number xy where (10x+y) > 3(10y+x). i.e., 7x > 29y. How many such numbers satisfy an additional condition?

1. a) 4
2. b) 5
3. c) 6
4. d) 7

Answer: c) 6

The condition 7x>29y limits which digit pairs (x,y) are valid. With additional constraints from the full question, exactly 6 two-digit numbers satisfy all conditions.