Let $N$ be the smallest positive integer whose digits have a product of 2000 . The sum of the digits of $N$ is
(A) 21
(B) 23
(C) 25
(D) 27
(E) 29
Let $N$ be the smallest positive integer whose digits have a product of 2000 . The sum of the digits of $N$ is
(A) 21
(B) 23
(C) 25
(D) 27
(E) 29

## Solution

Since $2000=2^{4} \cdot 5^{3}$, the smallest possible positive integer satisfying the required conditions is 25558 which gives the sum $2+5+5+5+8=25$. A natural answer might be 23 since 44555 satisfies the given conditions. However, since $25558<44555$ and the question requires the smallest number then the answer must be 25 and not 23 .

ANSWER: (C)