Lesson: 2 Equations with 2 Unknowns

Reinforcement Activities

The following practice questions were chosen to highlight the different ways the GMAT can test the concepts covered in the above video lesson. Brent, the course creator, has provided detailed solutions to most of the questions.

Comment on 2 Equations with 2 Unknowns

omat - November 5, 2019
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

gmat-admin - November 6, 2019

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.

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