Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 65

What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?

  1. 1063
  2. 1073
  3. 1083
  4. 1183

Answer

1083

We need a number N > 1000 such that dividing by 6, 9, 12, 15, 18 leaves remainder 3. So N - 3 must be divisible by all these numbers.

  • Key fact: (\text{LCM}(6,9,12,15,18)=180). Hence (N = 180k + 3).
  • Smallest such number greater than 1000: (180 \times 5 + 3 = 903) (too small), (180 \times 6 + 3 = 1083).

Option check:

  • (a) 1063: (1063-3=1060), not divisible by 9, 12, 15, 18. Incorrect.
  • (b) 1073: (1073-3=1070), not divisible by 6, 9, 12, 15, 18. Incorrect.
  • (c) 1083: (1083-3=1080), divisible by 6, 9, 12, 15, 18. Correct.
  • (d) 1183: (1183-3=1180), not divisible by 9, 12, 15, 18. Incorrect.
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