Multiple choice

The whole number (W) is divisible by 7. (W) leaves a remainder of 1 when divided by 2, 3, 4 or 5. What is the sum of the digits of the smallest value of (W)?\

  1. 4

  2. 2

  3. 7

  4. 3

  5. None of these
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A Correct answer
Explanation

W leaves remainder 1 when divided by 2, 3, 4, or 5, so W-1 must be divisible by LCM(2,3,4,5)=60. Thus W=60k+1. For W to be divisible by 7: 60k+1 ≡ 0 (mod 7). Since 60 ≡ 4 (mod 7), we get 4k ≡ 6 (mod 7), giving k=5 as smallest solution. W=301, sum of digits=4.

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