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(5-y)(y-5)

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(5-y)(y-5) [#permalink] New post 13 Aug 2019, 04:33
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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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Re: (5-y)(y-5) [#permalink] New post 13 Aug 2019, 05:21
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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: \(0\)

Answer: B

Cheers,
Brent
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Re: (5-y)(y-5) [#permalink] New post 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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Re: (5-y)(y-5) [#permalink] New post 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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