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

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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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:

92% (01:39) correct 7% (02:10) wrong based on 13 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
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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
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

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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Joined: 10 Apr 2015
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Kudos [?]: 1468 [1] , given: 8

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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Expert's post
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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 1543
Followers: 56

Kudos [?]: 1468 [0], given: 8

Re: If x2 – 2xy = 84 and x – y = –10, what is the value of |y|? [#permalink]  29 Jan 2019, 07:44
Expert's post
sandy wrote:
If $$x^2 - 2xy = 84$$ and $$x - y = -10$$, what is the value of |y|?

[Reveal] Spoiler: OA
4

Another approach is to use substitution

Given:
x - y = -10
x² - 2xy = 84

Solve the top equation for x to get: x = y - 10

Take the bottom equation and replace x with (y - 10) to get: (y - 10)² - 2(y - 10)y = 84
Expand left side to get: y² - 20y + 100 - 2y² + 20y = 84
Simplify: -y² + 100 = 84
Subtract 100 from both sides to get: -y² = -16
Divide both sides by -1 to get: y² = 16
Solve: y = 4 OR y = -4

In both cases, |y| = 4

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: If x2 – 2xy = 84 and x – y = –10, what is the value of |y|?   [#permalink] 29 Jan 2019, 07:44
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