योगफल S = x + y + z के संबंध में निम्नलिखित कथनों पर विचार कीजिए, जहाँ x, y और z में से प्रत्येक 10 से छोटी भिन्न अभाज्य संख्या है :
- 1.S का इकाई अंक 0 हो सकता है।
- 2.S का इकाई अंक 9 हो सकता है।
- 3.S का इकाई अंक 5 हो सकता है।
उपर्युक्त कथनों में से कौन-से सही हैं?
Read this question in English
Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10:
1. The unit digit of S can be 0.
2. The unit digit of S can be 9.
3. The unit digit of S can be 5.
Which of the statements given above are correct?
(a) 1 and 2 only · (b) 2 and 3 only · (c) 1 and 3 only · (d) 1, 2 and 3
उत्तर और व्याख्या · explanation in English
Answer: (c) केवल 1 और 3
The primes below 10 are 2, 3, 5 and 7, and three distinct ones can be chosen in only four ways, giving sums 10, 12, 14 and 15. Unit digits 0 and 5 occur; 9 does not.
- Primes less than 10: 2, 3, 5, 7. Choosing 3 distinct ones gives just 4 cases.
- 2 + 3 + 5 = 10; 2 + 3 + 7 = 12; 2 + 5 + 7 = 14; 3 + 5 + 7 = 15.
- Possible unit digits: 0, 2, 4, 5.
- So statements 1 (0) and 3 (5) are correct; statement 2 (9) is not.
- ✓ 1. 2 + 3 + 5 = 10 ends in 0.
- ✗ 2. None of the four possible sums (10, 12, 14, 15) ends in 9.
- ✓ 3. 3 + 5 + 7 = 15 ends in 5.
Remember · When the set is tiny, list every case (four sums here) instead of reasoning in general.
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). ·