# Social Distancing with Data Sufficiency Challenge! – Day 10

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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 = -1qs/qs = -1… Sufficient. The correct answer is (B).