The product of three positive integers is 42 . The sum of two of these integers is 9 . The third integer is
(A) 1
(B) 7
(C) 6
(D) 3
(E) 2
Solution 1

If the sum of two positive integers is 9 , the possible pairs are 1 and 8,2 and 7,3 and 6 , and 4 and 5 .

Of these pairs, the only one in which each number is a divisor of 42 is 2 and 7 .

Since the three positive integers have a product of 42 , then two of them must be 2 and 7 , so
the third is $42 \div(2 \times 7)=42 \div 14=3$.

## Solution 2

The possible sets of three positive integers which multiply to give 42 are $\{1,1,42\},\{1,2,21\}$, $\{1,3,14\},\{1,6,7\}$, and $\{2,3,7\}$.

The only one of these sets that contains two integers which add to 9 is $\{2,3,7\}$.

Therefore, the third number must be 3 .

ANSWER: (D)