Discussion
Let x be a number between 5000 and 5500 which when divided by 14, 16, 20 and 35, the remainders so obtained are 5, 7, 11 and 26, respectively. What is the sum of the digits of x ?
Answer: C
The digit sum is 9. The divisors minus the remainders are 14 - 5 = 9, 16 - 7 = 9, 20 - 11 = 9 and 35 - 26 = 9, so x + 9 is a common multiple of 14, 16, 20 and 35. Their LCM is 560. Between 5000 and 5500, x + 9 must lie between 5009 and 5509, and the only multiple of 560 there is 560 x 9 = 5040. So x = 5031. Check: 5031 divided by 14 leaves 5, by 16 leaves 7, by 20 leaves 11 and by 35 leaves 26. The digit sum is 5 + 0 + 3 + 1 = 9.
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