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xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1596 [0], given: 373

CAT Tests
xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z [#permalink] New post 20 May 2018, 14:13
Expert's post
00:00

Question Stats:

86% (00:30) correct 14% (00:46) wrong based on 50 sessions
Quantity A
Quantity B
\(xy^2z(x^2z + yz^2 - xy^2)\)
\(x^3y^2z^2 + xy^3z^3 - x^2y^4z\)


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.
[Reveal] Spoiler: OA

_________________

Sandy
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1 KUDOS received
Director
Director
Joined: 20 Apr 2016
Posts: 741
Followers: 6

Kudos [?]: 492 [1] , given: 86

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Re: xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z [#permalink] New post 28 Jun 2018, 16:31
1
This post received
KUDOS
sandy wrote:
Quantity A
Quantity B
\(xy^2z(x^2z + yz^2 - xy^2)\)
\(x^3y^2z^2 + xy^3z^3 - x^2y^4z\)


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.


Here;

In statement 1 : \(xy^2z(x^2z + yz^2 - xy^2)\) = \(x^3y^2z^2 + xy^3z^3 - x^2y^4z\) = statement 2

Hence option C
_________________

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1596 [0], given: 373

CAT Tests
Re: xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z [#permalink] New post 17 Jul 2018, 12:07
Expert's post
Explanation

In Quantity A, the term xy2z on the outside of the parentheses must be multiplied by each of the three terms inside the parentheses. Then simplify the expression as much as possible.

Taking one term at a time, the first is \(xy^2z \times x^2z = x^3y^2z^2\), because there are three factors of x, two factors of y, and two factors of z. Similarly, the second term is \(xy^2z \times yz^2 = xy^3z^3\) and the third is \(xy^2z \times (-xy^2) = -x^2y^4z\).

Adding these three terms together gives the distributed form of Quantity A: \(x^3y^2z^2 + xy^3z^3 - x^2y^4z\).

This is identical to Quantity B, so the two quantities are equal.
_________________

Sandy
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Re: xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z   [#permalink] 17 Jul 2018, 12:07
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