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# (5-y)(y-5)

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(5-y)(y-5) [#permalink]  13 Aug 2019, 04:33
Expert's post
00:00

Question Stats:

28% (00:27) correct 71% (00:33) wrong based on 14 sessions
$$y \neq 5$$

 Quantity A Quantity B $$(5-y)(y-5)$$ $$0$$

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

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GRE Instructor
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Kudos [?]: 2208 [1] , given: 27

Re: (5-y)(y-5) [#permalink]  13 Aug 2019, 05:21
1
KUDOS
Expert's post
Carcass wrote:
$$y \neq 5$$

 Quantity A Quantity B $$(5-y)(y-5)$$ $$0$$

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.

IMPORTANT: Notice that we can factor out -1 from one part of the expression: $$5-y=-1(-5+y)=-1(y-5)$$

So, $$(5-y)(y-5)=-1(y-5)(y-5)$$
$$=-1(y-5)^2$$

So, we get:
Quantity A: $$-1(y-5)^2$$
Quantity B: $$0$$

Since it must be the case that $$(y-5)^2$$ is POSITIVE (since we are SQUARING the value of y-5), we can be certain that $$-1(y-5)^2$$ is NEGATIVE.

So, we get:
Quantity A: some NEGATIVE number
Quantity B: $$0$$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Kudos [?]: 20 [0], given: 3

Re: (5-y)(y-5) [#permalink]  15 Aug 2019, 14:14
(5-y)(y-5) =5y-y^2-5y =10y-y^2

let y=-1, 10y-y^2= -10-1 =-11
y=1, 10y-y^2=10-1=9

So ans is D
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Kudos [?]: 11 [0], given: 1

Re: (5-y)(y-5) [#permalink]  15 Aug 2019, 23:34
The expression can be written as $$-(5-y)(5-y)= -(5-y)^2$$
Square of (5-y) is positive and the whole expression will be negative because of '-' sign. Hence the answer is B
Re: (5-y)(y-5)   [#permalink] 15 Aug 2019, 23:34
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