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CSAT · 140 questions

Number system

Every UPSC CSAT question on this topic, 2016–2026, newest first. Tap an option to check yourself; the answer and explanation open below it.

Number system questions per year: 2016: 3, 2017: 7, 2018: 5, 2019: 13, 2020: 19, 2021: 10, 2022: 13, 2023: 21, 2024: 15, 2025: 22, 2026: 12 Asked in 11 of 11 years · most in 2025 (22)

UPSC syllabus: “Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation (charts, graphs, tables, data sufficiency etc. — Class X level);” See the full syllabus →

CSAT 2016 · Q13

Easy

There are five hobby clubs in a college — photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?

Answer & explanation

Answer: (d) 3

All five clubs meet together on days that are common multiples of 2, 3, 4, 5 and 6, that is every LCM = 60 days. Within 180 days that happens on days 60, 120 and 180 — three times.

  1. All five meet on a day that is a multiple of 2, 3, 4, 5 and 6.
  2. LCM(2, 3, 4, 5, 6) = 60.
  3. Within 180 days: days 60, 120 and 180 — 3 times.

Remember · Events repeating every a, b, c … days coincide every LCM(a, b, c …) days.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q29

Easy

In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of Rs. 2 by one student only, the total collection is Rs. 443. Then how many students are there in the class?

Answer & explanation

Answer: (b) 21

If there are n students, each gives Rs. n, so the collection is n². With the extra Rs. 2 it is 443, so n² = 441 and n = 21.

  1. n students each give Rs. n: total = n².
  2. n² + 2 = 443, so n² = 441 and n = 21.
  3. Check: 21 × 21 = 441; 441 + 2 = 443.

Remember · 'As many rupees as the number of people' makes the total a perfect square — look for the square near the figure.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q62

Easy

If R and S are different integers both divisible by 5, then which of the following is not necessarily true?

Answer & explanation

Answer: (b) R + S is divisible by 10

Write R = 5a and S = 5b. The difference, product and sum of squares always keep the factor 5 (or 25), but R + S = 5(a + b) is a multiple of 10 only when a + b is even — 5 + 10 = 15 shows it can fail.

  1. Let R = 5a and S = 5b, where a and b are different integers.
  2. R − S = 5(a − b), R × S = 25ab and R² + S² = 25(a² + b²): always true.
  3. R + S = 5(a + b) is divisible by 10 only if a + b is even. Counter-example: R = 5, S = 10 gives 15.
  • ✗ (a) R − S = 5(a − b) is always a multiple of 5.
  • ✓ (b) Fails for R = 5, S = 10: the sum 15 is not divisible by 10.
  • ✗ (c) R × S = 25ab is always a multiple of 25.
  • ✗ (d) R² + S² = 25(a² + b²) is always a multiple of 5.

Remember · For 'not necessarily true', try one quick counter-example with the smallest numbers allowed.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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