*This series is designed to help you step up your Data Sufficiency practice while we all spend a little extra time at home during the coronavirus situation; I’m going to publish one practice Data Sufficiency question each day! You can choose to do all of them, or none of them. *

*Click on the tag “Social Distancing DS Challenge” at the bottom of this post to see all of the questions in this series! *

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #10**

Does the product *pqrs* equal -1?

(1) (pq)/(rs) = -1

(2) p = -1/q and r = 1/s

**Explanation**

For statement (1), there are plenty of combinations of values that either satisfy or do not satisfy the question presented. Simplified to: *pq* = –*rs* we can see that this information isn’t getting us anywhere: not sufficient. (Hint: if you’re having a tough time with this one, makeup some values for *p*, *q*, *r*, and *s*. Multiples of 1 with one or three values negative would, in fact, yield a “yes” answer;” however, replace those “1” values with “2” values and the answer is “no.”)

Statement (2) gives us more important info (Hint: remember that *p* = ^{p}/_{1}, and don’t be afraid to cross-multiply to solve or simplify). Since a number multiplied by its reciprocal equals 1, we can use this info to confirm that:

*pqrs* = ^{-1}/*q* × *q* × ^{1}/_{s} × *s* = ^{-1}^{qs}/_{qs} = -1… Sufficient. The correct answer is (B).

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