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x< 0 and y>0

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GMAT Club Legend
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x< 0 and y>0 [#permalink] New post 25 Aug 2018, 16:38
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Question Stats:

72% (00:49) correct 27% (00:26) wrong based on 33 sessions
\(x< 0\) and \(y>0\)

Quantity A
Quantity B
\(|x| - |y|\)
\(|x - y|\)


A) Quantity A is greater.
B) Quantity 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: x< 0 and y>0 [#permalink] New post 30 Aug 2018, 21:03
I got the answer D, can anyone explain the B as an answer.
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Re: x< 0 and y>0 [#permalink] New post 31 Aug 2018, 02:34
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IshanGre wrote:
I got the answer D, can anyone explain the B as an answer.


It is given that x<0 and y>0y

Quantity A is "|x|−|y|"

Now since x<0, value of |x| = -x and value of |y| is y

"|x|−|y|" = - x - y which can be written as -(x+y)

Quantity B is |x−y|

Since x is less than 0 and y is also negative the whole term is negative. Hence open it with a (-) sign

-(x-y) = -x+y

Quantity A is -x-y
Quantity B is -x+y

Since y is greater than 0, Quantity B is greater than Quantity A

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Re: x< 0 and y>0 [#permalink] New post 31 Aug 2018, 06:01
The whole idea behind absolute value is to turn the value into positive no matter what the sign of the value is. x<0 and y>0 => |x|−|y| is positive x - positive y while |x−y| = |negative+negative| = positive x + positive y => B is greater.
Re: x< 0 and y>0   [#permalink] 31 Aug 2018, 06:01
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