Multiple choice

What is the sum of the digits of the least number, which when divided by 15, 25 and 27 leaves the same remainder 9 in each case and is also completely divisible by 11?

  1. 18

  2. 19

  3. 17

  4. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number leaves remainder 9 when divided by 15, 25, 27, so it's of the form LCM(15,25,27)k + 9 = 675k + 9. We need the smallest such number divisible by 11. Testing k=1: 675 + 9 = 684, which is divisible by 11 (684 = 11 × 62). Sum of digits of 684 = 6 + 8 + 4 = 18. Option A is correct.

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