Is pqrst > 0 ? (1) p - qrst = 0 (2) pqr/st > 0

With five variables to track, this one can seem tricky, but we should take the time to grasp just what is being tested before we jump in. Then, the problem will prove much simpler.

• If any unknown is 0, the product will be 0
• The product will be negative only if an odd number of variables (1, 3, or all 5) are negative (and none are 0)

If we keep just these two considerations in mind, we can arrive at an accurate conclusion within a short time.

Statement (1)

\(p - qrst = 0\)

We have no way of telling whether p = 0 and any of q, r, s, or t is also 0; or whether p is positive and there are an even number of negative variables in qrst (including none). Since the product pqrst can be either 0 or greater than 0, Statement (1) is NOT sufficient.

Statement (2)

\(\frac{pqr}{st} > 0\)

Because the left-hand side is positive, we know that no variable can be 0. We also know that we are dealing with either a positive over a positive (i.e. two or zero negatives in both the numerator and denominator) or a negative over a negative (i.e. one or three negatives in the numerator and one negative in the denominator). Either way, pqrst comes out positive, since there must be an even number of negatives (again, including the possibility that there are none at all). Thus, Statement (2) is sufficient, and the answer is (B).

Many inequalities test little more than basic interactions between positives, negatives, and/or 0. Keep your approach simple.

- Andrew