CAPF AC 2023 Q45: General Mental Ability – Quantitative Aptitude
- (a) 1611
- (b) 2701
- (c) 4031
- (d) 5603
Answer: (b) 2701
Explanation
Two-digit primes with reversed digits
Given: x and y are two-digit primes, y is x with the digits swapped, and x − y = 36.
How to think: write x = 10a + b and y = 10b + a.
Then x − y = 9(a − b) = 36, so a − b = 4.
Only a few digit pairs have a difference of 4, and primes are easy to test among them.
| a, b | x | y | Both prime? |
|---|---|---|---|
| 5, 1 | 51 = 3 × 17 | 15 | No |
| 6, 2 | 62 | 26 | No (even) |
| 7, 3 | 73 | 37 | Yes |
| 8, 4 | 84 | 48 | No (even) |
| 9, 5 | 95 | 59 | No (95 = 5 × 19) |
So x = 73, y = 37, and 73 − 37 = 36.
xy = 73 × 37 = 73 × 30 + 73 × 7 = 2190 + 511 = 2701.
Answer: (b) 2701.
Why each option is right or wrong
- (a) Incorrect. 1611 is not 73 × 37.
- (b) CORRECT. x = 73, y = 37, so xy = 2701.
- (c) Incorrect. 4031 is not 73 × 37.
- (d) Incorrect. 5603 is not 73 × 37.
Key point
x = 10a + b, y = 10b + a, x − y = 9(a − b) = 36, a − b = 4. Only 73 and 37 are both prime. Product 73 × 37 = 2701.
Remember
9(a − b) = 36 gives a − b = 4: 73 and 37.
Common mistakes
- Forgetting that both numbers must be prime; 51 and 95 fail.
- Using x + y instead of x − y (which gives a multiple of 11, not of 9).
- Computing 73 × 37 wrongly; split it as 73 × 30 + 73 × 7.
Exam tip
Educated guess: a quick option check: the last digit of xy equals the last digit of 3 × 7 = 21, which is 1. Only (a) 1611 and (b) 2701 end in 1, and 73 × 37 is about 2700, so (b).
Sources
- NCERT Class VI Mathematics — Playing with Numbers, Chapter 3 (prime numbers)
- NCERT Class X Mathematics — Real Numbers, Chapter 1 (prime factorisation)