## What is the value of r^2âˆ’2rs+s^2?

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### What is the value of r^2âˆ’2rs+s^2?

by Vincen » Mon Oct 02, 2017 9:55 am
What is the value of r^2âˆ’2rs+s^2?

(1) s=4
(2) râˆ’s=12

The OA is B.

How can I use statement (2) to know the value of r^2âˆ’2rs+s^2?

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by Brent@GMATPrepNow » Mon Oct 02, 2017 10:04 am
Vincen wrote:What is the value of rÂ² âˆ’ 2rs + sÂ²?
(1) s = 4
(2) r âˆ’ s = 12
Target question: What is the value of rÂ² âˆ’ 2rs + sÂ²?
This is a good candidate for rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Notice that rÂ² âˆ’ 2rs + sÂ² is one of the special quadratic expressions
It can be factored as follows: rÂ² âˆ’ 2rs + sÂ² = (r - s)(r - s) = (r - s)Â²
So....REPHRASED target question: What is the value of (r - s)Â² ?

Statement 1: s = 4
Since there's no information about r, there's no way to determine the value of (r - s)Â²
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: r âˆ’ s = 12
PERFECT!!
This means that (r - s)Â² = (12)Â² = 144
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

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