What is the value of . . . . . . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Thu Jan 18, 2018 7:10 am

What is the value of $$r^2âˆ’2rs+s^2?$$ (1) s=4
(2) râˆ’s=12

The OA is the option B.

How can I use the statement (2) to get an answer? Experts, I'd like your explanation. Thanks in advanced.

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Source: Beat The GMAT — Data Sufficiency | Thu Jan 18, 2018 7:10 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 18, 2018 7:17 am

VJesus12 wrote:What is the value of $$r^2âˆ’2rs+s^2?$$
(1) s=4
(2) râˆ’s=12

The OA is the option B.

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 a "special product"
It can be factored as follows: rÂ² âˆ’ 2rs + sÂ² = (r - s)(r - s) = (r - s)Â²

REPHRASED target question: What is the value of (r - s)Â²?

Statement 1: s=4
No information about r, so statement 1 is NOT SUFFICIENT

Statement 2: r âˆ’ s =12
This means (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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