Discussion
Let x be the least number which when divided by 8, 12, 20, 28, 35 leaves a remainder 5 in each case. What is the sum of digits of x ?
Answer: D
The sum of the digits of x is 17.
A number leaving remainder 5 when divided by each of 8, 12, 20, 28 and 35 is 5 more than a common multiple of them. The least such number uses their LCM:
\[ \begin{aligned} 8 &= 2^{3},\ 12 = 2^{2} \cdot 3,\ 20 = 2^{2} \cdot 5 \\ 28 &= 2^{2} \cdot 7,\ 35 = 5 \cdot 7 \\ \text{LCM} &= 2^{3} \cdot 3 \cdot 5 \cdot 7 = 840 \\ x &= 840 + 5 = 845 \end{aligned} \]
The digit sum is 8 + 4 + 5 = 17. Forgetting to add the remainder gives 840, digit sum 12, which is not an option; 11, 14 and 15 come from other slips.
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