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

[zenithexe]

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

(1) (x + y)(x – y) = 5
(2) xy = 6


I have no idea how to solve this one, any help is appreciated. Thanks

[tohellandback]

IMO A
1)( x + y)(x – y) = 5
possibilities:
(x+y)=1 ,(x-y)=5- rejected because x and y are negative
(x+y)=5 ,(x-y)=1, rejected for the same reason

(x+y)=-1 ,(x-y)=-5, if x+y=-1 x=-y-1, now x has to be negative. for any value of y<0, it is impossible. so rejected
(x+y)=-5 ,(x-y)=-1. SUFFICIENT

2)xy=6. x and y have to be negative. so one of them is -2 and other is -3 but we need to know which one is what. INSUFF

[zenithexe]

wow, never thought I'd see a guy/gal from Tokyo on this site. Its nice to know there is someone else studying for Gmat in Japan.

Thanks for the solution, I get it now.

[tohellandback]

never thought I'd see a guy/gal from Tokyo on this site

umm, why not??

[zenithexe]

Coz I did search for Tokyo (or was it Japan) on "Let's meet up" section and I found none.

I guess I should pm for this kind of stuff, it's getting off the topic.

[benissleeping]

This was my thinking on the Q:

(1) Multiply out x^2 - y^2 = 5
Just by looking at this you can see it solves for x=-4 and y=-3 (16-9=5)
and x=-3 and y=-2 (9-4=5)

x-y = -1

(2) xy=6
x could be -6 and y -1 or x -3 and y -2. NS

So A

[zenithexe]

This was my thinking on the Q:

(1) Multiply out x^2 - y^2 = 5
Just by looking at this you can see it solves for x=-4 and y=-3 (16-9=5)
and x=-3 and y=-2 (9-4=5)

Thanks!
just out of curiosity how do you quickly come up with the numbers (X^2=16, Y^2=9)? and it there a way to be sure that those numbers are only numbers capable of satisfying the clause? I wish I could do that.

[tryin700]

Is it A

Given x<y<1

1) (x + y)(x – y) = 5

RHS = +5

so 2 combination are possible

-5X-1 or -1X-5

this means x=-3 and y=-2

SUFF

2) xy=6
possible cases -1 and -6 or -3 or -2

INSUFF

Hence A

[ogbeni]

Why is statement 1 sufficient when (X-Y) could be either -1 or -5? I eliminated statement 1 based on those 2 possibilities.

Look forward to getting an explanation! Thnx

[matanga]

Why is statement 1 sufficient when (X-Y) could be either -1 or -5? I eliminated statement 1 based on those 2 possibilities.

Look forward to getting an explanation! Thnx

Because you have 2 negative numbers, and, since y>x, when you subtract y from x, you are technically adding a value to x to make it closer to 0. Had the question not stated y was negative, then your logic would have been correct.


Hope this helps !

[ogbeni]

Oh i get it now. The fact that x<y<0 limits the possibilities of x and y to x = -3 and y = -2.

My goodness!! With the time pressure on the GMAT and without considering values for x and y, I just reasoned that the values of (x+y) x (x-y) could be -5,-1 or -1, -5 therefore eliminate - ARRGHHHH I hate that!!!!!!! lol

Thanks for clarifying