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If r - s = 240, does r = 320?

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Source: — Data Sufficiency |

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Re: If r - s = 240, does r = 320?

by Brent@GMATPrepNow » Thu May 21, 2020 9:10 am
BTGModeratorVI wrote: ↑
Sat May 16, 2020 7:30 am
 If r − s = 240, does r = 320?

(1) r = 4s
(2) s = 80

Answer: D
Source: Princeton Review
Given: r − s = 240

Target question: Does r = 320?

Statement 1: r = 4s

When we add this information to our given information we have two equations:
r − s = 240
r = 4s

There are several different approaches we can take from here.

One approach this to recognize that, since we have a system of 2 linear equations with 2 variables, we COULD solve the system for r and for s, which means we COULD answer the target question with certainty.
So, statement 1 is SUFFICIENT
---------
Another approach is to actually solve the system. How to do that also (for "fun")
Take: r − s = 240
Replace r with 4s to get: 4s - s = 240
Simplify to get: 3s = 240
Divide both sides by 3 to get: s = 80
Now take r = 4s, and replace s with 80 to get: r = 4(80) = 320
So, r = 320
So, statement 1 is SUFFICIENT

Statement 2: s = 80
Take the given equation, r − s = 240, and replace s with 80 to get: r − 80 = 240
Solve the equation to get r = 320
So, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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