The number 3798125P369 is divisible by 7. What is the value of the digit P?

Answer: (b) 6

Because 1001 = 7 × 11 × 13, a number is divisible by 7 when the alternating sum of its three-digit groups (taken from the right) is. That sum here is 1063 − P, and 1063 leaves remainder 6 on division by 7, so P = 6.

1. Since 1001 = 7 × 11 × 13, a number is divisible by 7 if the alternating sum of its 3-digit groups, taken from the right, is divisible by 7.
2. Groups of 3798125P369 from the right: 369, 25P, 981, 37.
3. Alternating sum = 369 − 25P + 981 − 37 = 1313 − (250 + P) = 1063 − P.
4. 1063 = 7 × 151 + 6, so 1063 − P is a multiple of 7 only when P = 6.
5. Check: 37981256369 ÷ 7 = 5425893767 exactly.

Remember · For divisibility by 7, 11 or 13 in a long number, take the alternating sum of 3-digit groups from the right (1001 = 7 × 11 × 13).

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error