If x and y are integers such that x

Question

If x and y are integers such that x < y < 0 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

Bunuel · Accepted Answer

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.

subhashghosh · Answer

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 ?

nfjet · Answer

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.

calreg11 · Answer

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

alex1233 · Answer

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.

Bunuel · Answer

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.

hfbamafan · Answer

Are we allowed to multiply Statement 2 by -1?

Bunuel · Answer

Yes, we can do that. But why?

TheKingInTheNorth · Answer

How come this is a 700 level question ?

GMATinsight · Answer

Please check the solution as attached

Answer: Option A

Prasannathawait · Answer

An excellent question that wants us to come out of conventional thinking to solve any question.
I got it wrong. Marked C.
But after reading the explanations realized that I have to be more cautious before answering the questions. This is a common trap of GMAT. Should be aware of it.

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

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