Multiple choice

Which of the following options is the largest 4-digit number, which when divided by 15, leaves a remainder of 12 and when divided by 8, leaves a remainder of 5?

  1. 9975

  2. 9957

  3. 9945

  4. 9917

  5. 9996

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B Correct answer
Explanation

We need a number N such that N = 15k + 12 and N = 8m + 5. This implies N + 3 is divisible by 15 and 8. The LCM of 15 and 8 is 120. So N + 3 = 120k, or N = 120k - 3. For the largest 4-digit number, 120k - 3 <= 9999, so 120k <= 10002, k = 83. N = 120 * 83 - 3 = 9960 - 3 = 9957.