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

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If x and y are integers such that x < y < 0 what is x - y? [#permalink] New post 08 Mar 2012, 21:04
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If x and y are integers such that x < y < 0 what is x - y ?

(1) (x + y)(x - y) = 5
(2) xy = 6

[Reveal] Spoiler:
How would you do this question?

also is it wrong to make statement 1) (x+y)(x-y)=5 into x^2-y^2=5

and then square root both sides to make x-y=√5 ??

please advise... I know another method of getting it right, but I want to confirm if the above can be mathematically done
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Re: Need Help with Math Concept [#permalink] New post 09 Mar 2012, 00:14
shawndx wrote:
If X and Y are integers such that x<y<0m what is x-y?

1) (x+y)(x-y)=5
2) xy= 6

How would you do this question?

also is it wrong to make statement 1) (x+y)(x-y)=5 into x^2-y^2=5

and then square root both sides to make x-y=√5 ??



please advise... I know another method of getting it right, but I want to confirm if the above can be mathematically done


This portion in the above highlighted section is absolutely wrong because (x-y)^2 = x^2 - 2xy + y^2 and you cannot take square root of x^2 - y^2 as x-y.

I'm not solving it, but it is obvious that the answer is C or E.
What is the method you're having in your mind ?


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Re: Need Help with Math Concept [#permalink] New post 09 Mar 2012, 02:03
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A.) First distribute (x+y)(x-y)=5 to get (x^2)-xy+xy-(y^2)=5.
The -xy and +xy cancel each other out so that you now have (x^2)-(y^2)=5.
The question tells us that both x and y are negative (x<y<0) and are integers. From that point you can easliy determine two squares whose difference is 5. And since the question tells us the absolute value of x>y, then x=-3 and y=-2. Sufficient.

B.) The question tells us that the two variables represent negative integers(x<y<0). B tells us that xy=6, which gives us two differnt pairs of integers for x and y: (-1x-6) and (-2x-3). Insufficient.


Answer A.
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Re: If X and Y are integers such that x<y<0 what is x-y? [#permalink] New post 09 Mar 2012, 04:37
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If x and y are integers such that x<y<0 what is x-y?

(1) (x+y)(x-y)=5. 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 5. There are only two combination of such factors possible: (1, 5) and (-1, -5). Since given that x and y are both negative then the first case is out, so x-y is either -1 or -5, but it can not be -5, because in this case x+y must be -1 and no sum of two negative integers yields -1. Hence x-y=-1. Sufficient.

(2) xy= 6. If x=-3 and y=-2 then x-y=-1 but if x=-6 and y=-1 then x-y=-5. Not sufficient.

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-y? [#permalink] New post 16 Apr 2012, 18:49
great answer guys.
It is important to look at it a different way other than just trying to go brute algebra. It's hard to go out of that mindset once you are so used to just solving all other problems that way. Thanks
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Re: If X and Y are integers such that x<y<0 what is x-y? [#permalink] New post 09 Mar 2013, 06:29
Bunuel wrote:
If x and y are integers such that x<y<0 what is x-y?

(1) (x+y)(x-y)=5. 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 5. There are only two combination of such factors possible: (1, 5) and (-1, -5). Since given that x and y are both negative then the first case is out, so x-y is either -1 or -5, but it can not be -5, because in this case x+y must be -1 and no sum of two negative integers yields -1. Hence x-y=-1. Sufficient.

(2) xy= 6. If x=-3 and y=-2 then x-y=-1 but if x=-6 and y=-1 then x-y=-5. Not sufficient.

Answer: A.

Hope it's clear.


In these type of questions such how do we know that in statement A we must have only 2 possible combinations? My GMAT "instinct" lead me to choose A but it I can not think of a logical way to prove that there must be for sure only 2 combinations.
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Re: If X and Y are integers such that x<y<0 what is x-y? [#permalink] New post 10 Mar 2013, 05:13
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alexpavlos wrote:
Bunuel wrote:
If x and y are integers such that x<y<0 what is x-y?

(1) (x+y)(x-y)=5. 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 5. There are only two combination of such factors possible: (1, 5) and (-1, -5). Since given that x and y are both negative then the first case is out, so x-y is either -1 or -5, but it can not be -5, because in this case x+y must be -1 and no sum of two negative integers yields -1. Hence x-y=-1. Sufficient.

(2) xy= 6. If x=-3 and y=-2 then x-y=-1 but if x=-6 and y=-1 then x-y=-5. Not sufficient.

Answer: A.

Hope it's clear.


In these type of questions such how do we know that in statement A we must have only 2 possible combinations? My GMAT "instinct" lead me to choose A but it I can not think of a logical way to prove that there must be for sure only 2 combinations.


Given that (x+y)(x-y)=5. Since x and y are integers, then we have that the product of 2 multiples is equal to 5.

Now, 5 can be broken into a product of 2 multiples only in 2 ways: 5=1*5 or 5=(-1)*(-5). After that you can refer to the solution above to see how it comes that x-y=-1.

Hope it helps.
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Re: If X and Y are integers such that x<y<0 what is x-y? [#permalink] New post 06 Dec 2013, 00:36
Are we allowed to multiply Statement 2 by -1?
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Re: If X and Y are integers such that x<y<0 what is x-y? [#permalink] New post 06 Dec 2013, 01:48
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Re: If X and Y are integers such that x<y<0 what is x-y?   [#permalink] 06 Dec 2013, 01:48
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