Lesson: 2 Equations with 2 Unknowns

Comment on 2 Equations with 2 Unknowns

Hi Brent, could you offer some insight into one of the questions you have linked above?

Is rst = 1 ?

(1) rs = 1
(2) st = 1

It's clear to me why either statement alone is insufficient.

However, when combining them, I substituted the value or r from statement 1 (r = 1/s) into statement 2... essentially, I got both s and t in terms of r, that is, s = 1/r and t = r.

This makes the product rst = (r)(1/r)(r) = r.
This led me to picking E as the answer. Is this valid? All solutions of this question point towards creating tables with counter examples.
gmat-admin's picture

Question link: https://gmatclub.com/forum/is-rst-90398.html

Your solution is perfectly valid.
However, once you conclude that rst = r, it's important that you confirm that r may or may not equal 1.
If it's the case that r MUST equal 1, then the combined statements are sufficient.
If it's the case that r can be ANY value, then the combined statements are not sufficient.

Hi Brent,

Please do you have any advice on how to improve speed? I usually can solve most problems but the harder ones I solve over 2 minutes. :(

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