किसी विद्यालय में प्रत्येक विद्यार्थी को एक विशिष्ट पहचान संख्या नियत की गई है । एक विद्यार्थी फुटबाल का खिलाड़ी है यदि और केवल यदि पहचान संख्या 4 से विभाज्य है, जबकि एक विद्यार्थी क्रिकेट का खिलाड़ी है यदि और केवल यदि पहचान संख्या 6 से विभाज्य है । यदि 1 से 100 तक की प्रत्येक संख्या किसी न किसी विद्यार्थी के लिए नियत की गई है, तो उनमें से कितने विद्यार्थी क्रिकेट के साथ-साथ फुटबाल भी खेलते हैं ?
Read this question in English
In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football?
(a) 4 · (b) 8 · (c) 10 · (d) 12
उत्तर और व्याख्या · explanation in English
Answer: (b) 8
A student plays both games only if the number is divisible by both 4 and 6, that is by their LCM 12. There are 8 multiples of 12 up to 100.
- Divisible by 4 and by 6 ⇔ divisible by LCM(4, 6) = 12.
- Multiples of 12 from 1 to 100: 12, 24, 36, 48, 60, 72, 84, 96.
- Count = 8 (100 ÷ 12 = 8 remainder 4).
- Check: using 24 (= 4 × 6) would wrongly drop 12, 36, 60 and 84.
Remember · 'Divisible by a and by b' means divisible by LCM(a, b), not a × b.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·