Multiple choice

The greatest number of four digits which when divided by 12, 16 and 24 leave remainders 2, 6 and 14 respectively is

  1. 9974

  2. 9970

  3. 9807

  4. 9998
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A Correct answer
Explanation

We need N such that N = 12a + 2 = 16b + 6 = 24c + 14. This means N - 10 is divisible by LCM(12, 16, 24) = 48. Largest 4-digit multiple of 48 is 9984. Adding 10 gives 9994, but 9994 - 48 = 9946 doesn't work. Testing backwards: 9974 satisfies all conditions (9974/12 = 831r2, /16 = 623r6, /24 = 415r14).

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