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# |x-y|=? 1) x and y are integers 2) xy=5

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7363
GMAT 1: 760 Q51 V42
GPA: 3.82
|x-y|=? 1) x and y are integers 2) xy=5  [#permalink]

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07 Sep 2017, 01:46
00:00

Difficulty:

35% (medium)

Question Stats:

69% (00:57) correct 31% (00:29) wrong based on 55 sessions

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[GMAT math practice question]

|x-y|=?

1) x and y are integers
2) xy=5

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Math Expert
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Posts: 7684
Re: |x-y|=? 1) x and y are integers 2) xy=5  [#permalink]

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07 Sep 2017, 02:30
MathRevolution wrote:
[GMAT math practice question]

|x-y|=?

1) x and y are integers
2) xy=5

Hi...

Nothing much out of statement I..
Statement II..
xy=5..
If x=1, y=5.....|x-y|=|1-5|=4
If x=1/5, y=25.....|x-y|=|1/5-25|=124/25
Insufficient

Let's see combined
X and y are INTEGERS and xy =5, which is a PRIME number.
Any prime number has ONLY 2 factors, 1 and itself..
So 5=1*5 or -1*-5
|x-y|=|1-5|=4......|5-1|=4.......|-1-(-5)|=4......|-5-(-1)|=4
All case ans is 4
Sufficient

C
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Math Revolution GMAT Instructor
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GPA: 3.82
Re: |x-y|=? 1) x and y are integers 2) xy=5  [#permalink]

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10 Sep 2017, 18:19
=>
1) It is not sufficient definitely.

2) x = 1, y = 2 and x = 2, y = 5/2
We don’t have a unique solution.

1) & 2)
We have the following cases.
x = 1, y = 5 / x = -1, y = -5 / x = 5, y = 1 / x = 1, y = 5
All of them have |x-y| = 4.
Thus we have a unique solution.
Both conditions together are sufficient.

Ans: C
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Re: |x-y|=? 1) x and y are integers 2) xy=5   [#permalink] 10 Sep 2017, 18:19
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