222³³³ + 333²²² is divisible by which of the following numbers?
- (a) 2 and 3 but not 37
- (b) 3 and 37 but not 2 ✓ UPSC's answer
- (c) 2 and 37 but not 3
- (d) 2, 3 and 37
Why the answer is (b)
• Divisibility by 2: 222³³³ is even and 333²²² is odd, so their sum is odd — not divisible by 2.
• Divisibility by 3: 222 and 333 are both multiples of 3, so both terms, and their sum, are divisible by 3.
• Divisibility by 37: 222 = 6 × 37 and 333 = 9 × 37, so both terms, and their sum, are divisible by 37.
• The number is divisible by 3 and 37 but not by 2 — option (b).
Why the other options are wrong
- (a) 2 and 3 but not 37
- The expression is not divisible by 2 because it is the sum of an even and an odd number.
- (c) 2 and 37 but not 3
- The expression is not divisible by 2, so any option claiming divisibility by 2 is incorrect.
- (d) 2, 3 and 37
- The expression is not divisible by 2, so it cannot be divisible by 2, 3, and 37 simultaneously.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.