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If x2 – 2xy = 84 and x – y = –10, what is the value of |y|?

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [1] , given: 396

If x2 – 2xy = 84 and x – y = –10, what is the value of |y|? [#permalink]  23 Jun 2018, 11:52
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Question Stats:

90% (01:14) correct 10% (02:10) wrong based on 10 sessions
If $$x^2 - 2xy = 84$$ and $$x - y = -10$$, what is the value of |y|?

[Reveal] Spoiler: OA
4

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Sandy
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Intern
Joined: 05 Jan 2018
Posts: 32
Followers: 0

Kudos [?]: 16 [0], given: 8

Re: If x2 – 2xy = 84 and x – y = –10, what is the value of |y|? [#permalink]  25 Jun 2018, 07:00
Ans. 4
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1650 [0], given: 396

Re: If x2 – 2xy = 84 and x – y = –10, what is the value of |y|? [#permalink]  28 Jul 2018, 16:11
Expert's post
Explanation

One of the “special products” you need to memorize for the exam is $$x^2 – 2xy + y^2 = (x – y)^2$$.

Write this pattern on your paper and plug in the given values:

$$x^2 - 2xy + y^2 = (x - y)^2$$
$$84 + y^2 = (-10)^2$$
$$84 + y^2 = 100$$
$$y^2 = 16$$
$$y = 4$$ or $$-4$$, so $$|y| = 4$$.
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Sandy
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GRE Instructor
Joined: 10 Apr 2015
Posts: 1227
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Kudos [?]: 1105 [1] , given: 7

Re: If x2 – 2xy = 84 and x – y = –10, what is the value of |y|? [#permalink]  03 Aug 2018, 12:41
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sandy wrote:
If $$x^2 - 2xy = 84$$ and $$x - y = -10$$, what is the value of |y|?

[Reveal] Spoiler: OA
4

Given:
x - y = -10
x² - 2xy = 84

Take top equation and square both sides to get: (x - y)² = (-10)²
Expand and simplify: to get: x² - 2xy + y² = 100

We now have:
x² - 2xy + y² = 100
x² - 2xy = 84

Subtract bottom equation from top equation to get: y² = 16
So, EITHER y = 4 OR y = -4

In both cases, |y| = 4

Answer: \$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: If x2 – 2xy = 84 and x – y = –10, what is the value of |y|?   [#permalink] 03 Aug 2018, 12:41
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