The number 1000 can be written as the product of two positive integers, neither of which contains zeros. The sum of these two integers is
(A) 65
(B) 110
(C) 133
(D) 205
(E) 1001
We know that $1000=10 \times 10 \times 10=2 \times 5 \times 2 \times 5 \times 2 \times 5$. To write 1000 as the product of two integers neither of which contains a 0 , we must ensure that neither has a factor of 10 . This tells us that we want to separate the factors of 2 and the factors of 5 , ie.

$1000=2 \times 2 \times 2 \times 5 \times 5 \times 5=8 \times 125$, and $8+125=133$.

ANSWER: (C)