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