Bunuel wrote:
If \(a\), \(b\), and \(c\) are 3 different integers and \(a * b * c = 55\), what is the value of c?
(1) a = 5
(2) b = 11
For this problem, I found it useful to start by creating a factor tree. 55 breaks down into 5 x 11, both prime numbers, so the only integer left has to be 1. The rest of the question deals with how negatives and positives interact, since it would not be safe to assume that
integers means only positive ones.
Statement (1), as the official solution points out, tells us nothing about "b," so we cannot speculate on which of the other integers "c" may be. Out go (A) and (D).
Statement (2) also reveals nothing about one of the other two unknowns, this time "a," so we are in the same boat as before. (B) is out.
Taken together, we know a * b * c = 55 and, by substitution, that (5) * (11) * c = 55. We could solve this one algebraically, but there is no need, once we understand that a positive times a positive times some unknown to yield a positive product must mean that the unknown is positive itself. Thus, "c" can only be 1, and (C) is the answer.