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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 2018 · Q2

Easy

Consider the following sum:

• + 1• + 2• + •3 + •1 = 21•

In the above sum, • stands for

Answer & explanation

Answer: (d) 8

Treat • as one digit x and write every term by place value. The equation 23x + 34 = 210 + x gives x = 8.

  1. Let • = x. Then 1• = 10 + x, 2• = 20 + x, •3 = 10x + 3, •1 = 10x + 1 and 21• = 210 + x.
  2. Left side: x + (10 + x) + (20 + x) + (10x + 3) + (10x + 1) = 23x + 34.
  3. 23x + 34 = 210 + x, so 22x = 176 and x = 8.
  4. Check: 8 + 18 + 28 + 83 + 81 = 218, which is 21• with • = 8.

Remember · Write each symbol-number by place value (tens digit × 10 + units digit), then solve one linear equation.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2018 · Q23

Easy

If X is between −3 and −1, and Y is between −1 and 1, then X² − Y² is in between which of the following?

Answer & explanation

Answer: (d) 0 and 9

Squaring removes the signs: X² lies between 1 and 9, and Y² between 0 and 1. So X² − Y² is more than 1 − 1 = 0 and less than 9 − 0 = 9.

  1. −3 < X < −1 gives 1 < X² < 9.
  2. −1 < Y < 1 gives 0 ≤ Y² < 1.
  3. Smallest value of X² − Y²: just above 1 − 1 = 0. Largest: just below 9 − 0 = 9.
  4. So X² − Y² lies between 0 and 9.
  5. Check: X = −2.9 and Y = 0 give 8.41, more than 8, so (c) is too narrow.

Remember · For the range of a difference, pair the largest first term with the smallest second term and vice versa; square before combining.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2018 · Q24

Easy

X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?

Answer & explanation

Answer: (a) XY

With X at least 2, the product XY is at least 2Y, while Y/X is at most Y/2, X/Y is below 1 and (X + Y)/XY is below 1. XY is always the largest.

  1. Try the smallest values X = 2, Y = 3: XY = 6, X/Y ≈ 0.67, Y/X = 1.5, (X + Y)/XY = 5/6.
  2. In general X ≥ 2, so XY ≥ 2Y > Y > Y/X.
  3. X/Y < 1 because Y > X, and (X + Y)/XY = 1/X + 1/Y ≤ 1/2 + 1/3 < 1.
  4. So XY is the largest.

Remember · For 'which is largest' under conditions, test the smallest allowed values first, then confirm with a general inequality.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2018 · Q34

Easy

A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first and last digits is greater than the number itself by 198, then the difference between the first and last digits is

Answer & explanation

Answer: (b) 2

Swapping the first and last digits of a three-digit number changes it by 99 × (difference of those digits). 198 ÷ 99 = 2, so the digits differ by 2 — the number is 103, which becomes 301.

  1. Let the number be 100a + c (middle digit 0); interchanged, it is 100c + a.
  2. (100c + a) − (100a + c) = 99(c − a) = 198, so c − a = 2.
  3. With a + c = 4: a = 1 and c = 3, so the number is 103.
  4. Check: 301 − 103 = 198.

Remember · Interchanging the end digits of a three-digit number changes it by 99 × their difference; divide the change by 99.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2018 · Q77

Easy

If x − y = 8, then which of the following must be true?

  1. 1.Both x and y must be positive for any value of x and y.
  2. 2.If x is positive, y must be negative for any value of x and y.
  3. 3.If x is negative, y must be positive for any value of x and y.

Select the correct answer using the code given below.

Answer & explanation

Answer: (d) Neither 1 nor 2 nor 3

y is always 8 less than x. When x is positive, y can be positive or negative (x = 10, y = 2; x = 2, y = −6), and when x is negative, y is even more negative. None of the three statements must hold.

  1. Rewrite the condition as y = x − 8.
  2. x = 2 gives y = −6: both need not be positive.
  3. x = 10 gives y = 2: y need not be negative when x is positive.
  4. If x is negative, y = x − 8 is below −8, so y can never be positive.
  • ✗ 1. x = 2, y = −6 satisfies x − y = 8 with y negative.
  • ✗ 2. x = 10, y = 2 satisfies the equation with both positive.
  • ✗ 3. A negative x makes y = x − 8 even more negative, never positive.

Remember · For 'must be true' statements, one counter-example disproves each; express one variable in terms of the other first.

Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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