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TAGS: GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Evaluate (4x – 2y)(6x + 3y) = 18 [#permalink]
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Expert's post 00:00

Question Stats: 88% (00:50) correct 11% (01:09) wrong based on 109 sessions
$$(4x - 2y)(6x + 3y) = 18$$

 Quantity A Quantity B 6 $$4x^2 -y^2$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 6
Page: 81
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 135

Kudos [?]: 2085 , given: 397

Re: Evaluate (4x – 2y)(6x + 3y) = 18 [#permalink]
Expert's post
Explanation

The given equation $$(4x - 2y)(6x + 3y) = 18$$ can be simplified as follows.

Step 1: Note that $$(4x - 2y) = 2(2x - y)$$ and $$(6x + 3y) = 3(2x + y)$$, so the given equation can be rewritten as $$(2)(2x - y)(3)(2x + y) = 18$$.

Step 2: Dividing both sides of the rewritten equation by 6 gives $$(2x - y)(2x + y) = 3.$$

Step 3: Multiplying out the left side of the equation in Step 2 gives $$4x^2 - y^2 = 3$$.

Since Quantity B is $$4x^2 - y^2$$, it follows that Quantity A is equal to 3. Since Quantity A is 6, the correct answer is Choice A.
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Sandy
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Manager Joined: 22 Feb 2018
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Re: Evaluate (4x – 2y)(6x + 3y) = 18 [#permalink]
correct: A
(4x - 2y)(6x + 3y) = 18
24x^2 + 12xy - 12xy - 6y^2 = 18
24x^2 - 6y^2 = 18 divide by 6:
4x^2 - y^2 = 3
So we arrived at B! and it equals 3, which is less than A.

_________________ GRE Instructor Joined: 10 Apr 2015
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Re: Evaluate (4x – 2y)(6x + 3y) = 18 [#permalink]
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Expert's post
sandy wrote:
$$(4x - 2y)(6x + 3y) = 18$$

 Quantity A Quantity B 6 $$4x^2 -y^2$$

GIVEN: (4x - 2y)(6x + 3y) = 18

Factor each part to get: (2)(2x - y)(3)(2x + y) = 18

Rewrite as: (2)(3)(2x - y)(2x + y) = 18

Simplify: (6)(4x² - y²) = 18

Divide both sides by 6 to get: Simplify: 4x² - y² = 3

We get:
QUANTITY A: 6
QUANTITY B: 3

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails

Manager Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 119 , given: 22

Re: Evaluate (4x – 2y)(6x + 3y) = 18 [#permalink]
(4x-2y)(6x+3y) = 18
2*(2x-y)*3*(2x+y) = 18
6*(2x-y)(2x+y) = 18
(2x-y)(2x+y) = 6
(2x)^2 - y^2 = 6
4x^2 - y^2 = 6
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GRE Instructor Joined: 10 Apr 2015
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Kudos [?]: 2358 , given: 33

Re: Evaluate (4x – 2y)(6x + 3y) = 18 [#permalink]
Expert's post
Fatemeh wrote:
(4x-2y)(6x+3y) = 18
2*(2x-y)*3*(2x+y) = 18
6*(2x-y)(2x+y) = 18
(2x-y)(2x+y) = 6
(2x)^2 - y^2 = 6
4x^2 - y^2 = 6

Be careful. When we divide both sides by 6, the right side becomes 3 (not 6)

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails Re: Evaluate (4x – 2y)(6x + 3y) = 18   [#permalink] 12 Jun 2019, 07:32
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