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If x and y are integers such that x < y < 0 what is x?

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If x and y are integers such that x < y < 0 what is x? [#permalink]

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If x and y are integers such that x < y < 0 what is x?

(1) (x + y)(x - y) = 7
(2) xy = 12

Problem from GMAT Focus:


[Reveal] Spoiler:
Explanation for why A is the answer from GMAC goes something like this:
x^2-y^2=7
x^2=7+y^2
x=sqr root (7+y^2)
Then use trial and error to determine that y must be -3 and therefore x must be -4.
This doesn't make sense to me for the following reason:
If y=-3, then x=4 because a perfect square can never be negative... That's why I chose C as the answer instead.

Thoughts?
Thanks! I have never seen a problem like this before.
[Reveal] Spoiler: OA

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Re: If x and y are integers such that x < y < 0 what is x? [#permalink]

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New post 22 Jul 2013, 08:11
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If x and y are integers such that x<y<0 what is x?

(1) (x+y)(x-y)=7. x and y are integers means that both x+y and x-y are integers. So, we have that the product of two integer factors equal to 7. There are only two combination of such factors possible: (1, 7) and (-1, -7). Since given that x and y are both negative then the first case is out, so x-y is either -1 or -7, but it cannot be -7, because in this case x+y must be -1 and no sum of two negative integers yields -1. Hence x-y=-1 and x+y=-7. Solving gives x=-4 . Sufficient.

(2) xy=12. Clearly insufficient: consider (x, y)=(-12, -1) and (x, y)=(-4, -3).

Answer: A.

Hope it's clear.
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Re: If x and y are integers such that x < y < 0 what is x? [#permalink]

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Great explanation Bunuel! Very clear :)

Bunuel wrote:
If x and y are integers such that x<y<0 what is x?

(1) (x+y)(x-y)=7. x and y are integers means that both x+y and x-y are integers. So, we have that the product of two integer factors equal to 7. There are only two combination of such factors possible: (1, 7) and (-1, -7). Since given that x and y are both negative then the first case is out, so x-y is either -1 or -7, but it cannot be -7, because in this case x+y must be -1 and no sum of two negative integers yields -1. Hence x-y=-1 and x+y=-7. Solving gives x=-4 . Sufficient.

(2) xy=12. Clearly insufficient: consider (x, y)=(-12, -1) and (x, y)=(-4, -3).

Answer: A.

Hope it's clear.

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Re: If x and y are integers such that x < y < 0 what is x? [#permalink]

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New post 14 Mar 2016, 23:43
tricialin wrote:
Problem from GMAT Focus:

If x and y are integers such that x<y<0 what is x?

1) (x+y)(x-y)=7
2) xy=12


Explanation for why A is the answer from GMAC goes something like this:
x^2-y^2=7
x^2=7+y^2
x=sqr root (7+y^2)
Then use trial and error to determine that y must be -3 and therefore x must be -4.
This doesn't make sense to me for the following reason:
If y=-3, then x=4 because a perfect square can never be negative... That's why I chose C as the answer instead.

Thoughts?
Thanks! I have never seen a problem like this before.

It is given that x and y are integers and both are less than o. and x<y
(1) says product of two numbers = 7 (both numbers are either positive or negative)
Here both numbers are negative because sum of two negative numbers cannot be positive (x+y)
Also sum of two negative integers cannot produce a fraction.
There is only one possibility that is -7*-1=7
It implies x=-4 and y=-3

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Re: If x and y are integers such that x < y < 0 what is x? [#permalink]

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Re: If x and y are integers such that x < y < 0 what is x?   [#permalink] 28 Nov 2017, 16:09
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