a, b, and c are three distinct positive integers. What is the product abc?
1) a + b + c = 7
2) ab + bc + ca = 14
For Statement 1, if we make all of the integers greater than 1, the smallest that they can be is 2, 3 and 4.
2 + 3 + 4 = 9. That's already too big. So one of them has to be 1.
1 + 3 + 4 = 8 Too big.
Must be 1 + 2 + 4. So there is only one set that works, and Statement 1 is sufficient.
For Statement 2, if we make all of the integers greater than 1, the smallest that they can be is 2, 3, and 4.
Plugging in 2, 3 and 4, we get 6 + 12 + 8 = 26 Too big. So one must be 1.
If a is 1 then the equation becomes b + bc + c = 14
Hmm. I'm thinking 8 + 6. That works with b = 2 and c = 4. 2 + 8 + 4 = 14.
Can other numbers work? If b = 3 and c = 4, the sum is going to be greater than 14.
So the integers must be 1, 2 and 4. So Statement 2 is sufficient.
The correct answer is
D.
