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x< 0 and y>0

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Retired Moderator
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x< 0 and y>0 [#permalink] New post 25 Aug 2018, 16:38
Expert's post
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Question Stats:

65% (00:42) correct 34% (00:36) wrong based on 109 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
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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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Mudit
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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.
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Re: x< 0 and y>0 [#permalink] New post 07 Nov 2019, 09:41
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Expert's post
sandy wrote:
\(x< 0\) and \(y>0\)

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



Concept #1: If x < 0, then |x| = -x
For example: |-3| = -(-3) = 3
and |-11| = -(-11) = 11

Concept #2: If y > 0, then |y| = y
For example: |8| = 8
and |22| = 22

Concept #3: If x < 0 and y > 0 then x < 0 < y
This means x < y
So, if we subtract y from both sides, we get: x - y < 0
So, applying Concept #1, we can see that |x - y| = -(x - y)
Upon substitution, we get:

QUANTITY A: |x| - |y| = (-x) - y
QUANTITY B: -(x - y)

Simplify
QUANTITY A: -x - y
QUANTITY B: -x + y

Add x to both quantities to get:
QUANTITY A: -y
QUANTITY B: y

Add y to both quantities to get:
QUANTITY A: 0
QUANTITY B: 2y

Since y > 0, we know that 2y > 0

Answer: B

Cheers,
Brent
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Re: x< 0 and y>0   [#permalink] 07 Nov 2019, 09:41
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