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# If |x|-|y|=13, then which of the following can't be the value of x-y?

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Director
Joined: 19 Oct 2018
Posts: 880
Location: India
If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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24 Jun 2019, 21:52
2
1
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Difficulty:

95% (hard)

Question Stats:

40% (02:24) correct 60% (02:18) wrong based on 152 sessions

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If |x|-|y|=13, then which of the following can't be the value of x-y?

A. -9
B. -13
C. -17
D. -18
E. -29
Director
Joined: 19 Oct 2018
Posts: 880
Location: India
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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26 Jun 2019, 01:20
2
1
1.
|x-y|≥|x|-|y|
|x-y|≥ 13
x-y≥13 or x-y≤-13

2.
We can notice that all the options are -ve, hence x<0

If x<0 and y>0
and |x|-|y|=13
then x= -13-k and y= k, , where k is positive real number
x-y=-13-2k (less than -13)

If x<0 and y<0
then x= -13-k and y=-k
x-y=-13

You can use either approach.

nick1816 wrote:
If |x|-|y|=13, then which of the following can't be the value of x-y?

A. -9
B. -13
C. -17
D. -18
E. -29
Intern
Joined: 01 Jul 2018
Posts: 2
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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13 Jul 2019, 08:17

I think -18 and -9 both cant be value of x-y. Correct me if I am wrong.

Here -18 being an even number, can only be a difference of two odd numbers or two even numbers. However, 13 can only be a difference of OddEven or EvenOdd numbers.

I fail to understand how -18 can be a value of x-y? Please explain.
Senior Manager
Joined: 09 Aug 2017
Posts: 427
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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13 Jul 2019, 08:35
Same doubt is in my mind.

Karan0912 wrote:

I think -18 and -9 both cant be value of x-y. Correct me if I am wrong.

Here -18 being an even number, can only be a difference of two odd numbers or two even numbers. However, 13 can only be a difference of OddEven or EvenOdd numbers.

I fail to understand how -18 can be a value of x-y? Please explain.
Director
Joined: 19 Oct 2018
Posts: 880
Location: India
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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13 Jul 2019, 08:48
1
x and y can be any real numbers. They can be rational or irrational numbers. Never assume anything in GMAT exam, if it's not explicitly mentioned.
If x=-15.5 and y=2.5
|x|-|y|=13, and x-y=-18

Karan0912 wrote:

I think -18 and -9 both cant be value of x-y. Correct me if I am wrong.

Here -18 being an even number, can only be a difference of two odd numbers or two even numbers. However, 13 can only be a difference of OddEven or EvenOdd numbers.

I fail to understand how -18 can be a value of x-y? Please explain.

Posted from my mobile device
Intern
Joined: 25 Mar 2019
Posts: 2
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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13 Jul 2019, 08:53
Here we can see that the options are all negative. Hence x<0
According to given question |x|>|y| and x <= -13, y<=0 to get a value of 13.
Therefore x-y is always less than or equal to -13. Hence x-y cannot be -9.

SVP
Joined: 03 Jun 2019
Posts: 1542
Location: India
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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13 Jul 2019, 09:05
sunnapuajaykumar wrote:
Here we can see that the options are all negative. Hence x<0
According to given question |x|>|y| and x <= -13, y<=0 to get a value of 13.
Therefore x-y is always less than or equal to -13. Hence x-y cannot be -9.

|x|-|y|=13
if y<0 |y| = -y
|x| = -13-y

x-y = -13-2y<-13

IMO A
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Manager
Joined: 20 Apr 2019
Posts: 83
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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27 Jul 2019, 01:16
nick1816 wrote:
1.
|x-y|≥|x|-|y|
|x-y|≥ 13
x-y≥13 or x-y≤-13

2.
We can notice that all the options are -ve, hence x<0

If x<0 and y>0
and |x|-|y|=13
then x= -13-k and y= k, , where k is positive real number
x-y=-13-2k (less than -13)

If x<0 and y<0
then x= -13-k and y=-k
x-y=-13

You can use either approach.

nick1816 wrote:
If |x|-|y|=13, then which of the following can't be the value of x-y?

A. -9
B. -13
C. -17
D. -18
E. -29

How do I know that |x-y|≥|x|-|y| is true? Is this a general rule or how can I see it with the information given?
Director
Joined: 19 Oct 2018
Posts: 880
Location: India
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?  [#permalink]

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27 Jul 2019, 01:45
1
|x-y|≥|x|-|y|
It's true for every real number.
1. If x and y have opposite signs, |x-y|>|x|-|y|
2. If x and y have same signs and |x|>|y|, then |x-y|=|x|-|y|
3. If x and y have same signs and |x|<|y|, then |x-y|>|x|-|y|

Luca1111111111111 wrote:
nick1816 wrote:
1.
|x-y|≥|x|-|y|
|x-y|≥ 13
x-y≥13 or x-y≤-13

2.
We can notice that all the options are -ve, hence x<0

If x<0 and y>0
and |x|-|y|=13
then x= -13-k and y= k, , where k is positive real number
x-y=-13-2k (less than -13)

If x<0 and y<0
then x= -13-k and y=-k
x-y=-13

You can use either approach.

nick1816 wrote:
If |x|-|y|=13, then which of the following can't be the value of x-y?

A. -9
B. -13
C. -17
D. -18
E. -29

How do I know that |x-y|≥|x|-|y| is true? Is this a general rule or how can I see it with the information given?
Re: If |x|-|y|=13, then which of the following can't be the value of x-y?   [#permalink] 27 Jul 2019, 01:45
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