222³³³ + 333²²² is divisible by which of the following numbers?

Answer: (b) 3 and 37 but not 2

222 = 2 × 3 × 37 and 333 = 3² × 37, so both terms, and hence their sum, are divisible by 3 and 37. But 222³³³ is even and 333²²² is odd, so the sum is odd and not divisible by 2.

1. Factorise the bases: 222 = 2 × 3 × 37 and 333 = 3 × 3 × 37.
2. Both 222³³³ and 333²²² contain the factors 3 and 37, so their sum is divisible by 3 and by 37.
3. 222³³³ is even; 333²²² is odd (a power of an odd number stays odd). Even + odd = odd.
4. So the sum is divisible by 3 and 37 but not by 2.

Remember · Factorise the bases first: a sum is divisible by any factor common to both terms. Even + odd is always odd.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error