Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Asking whether the product cdef is less than zero is equivalent to asking whether one of the following cases holds: exactly three variables are positive (and the other one is not), or exactly one of the variables is positive. So the question can be rephrased this way: “Is there an odd number of positive variables among c, d, e, and f?”
Statement 1: INSUFFICIENT. Even powers of variables reveal nothing about the sign of the variable. Meanwhile, odd powers have the same sign. So this statement can be rephrased as ce < 0, which tells us that either c or e is negative; the other variable is positive. Exactly one of the variables is positive. However, we don’t know anything about the signs of d and f.
Statement 2: INSUFFICIENT. This statement can be rephrased as df > 0, which tells us that either both variables are positive, or neither variable is positive. However, we don’t know anything about the signs of c and e.
Statements 1 and 2 together: SUFFICIENT. Together, we know that either 1 or 3 of the variables are positive. Thus, we can answer the question with a definite “Yes.”
The correct answer is C.