Source: mgmat question bank
Equations and inequalities, #16
If x and y are nonzero integers, is (x^-1 + y^-1)^-1 > [(x-1)(y-1)]^-1 ?

(1) x = 2y
(2) x + y > 0

OA: A

Explanation:
(1) SUFFICIENT: If we plug x = 2y into our simplified question we get the following:

Is 2y^2/3y > 2y^2 ?
Since 2y^2 must be positive we can divide both sides of the inequality by 2y^2 which leaves us with the following:

Is 1/3y> 1 ?
If we investigate this carefully, we find that if y is an nonzero integer, 1/3y is never greater than 1. Try y = 2 and y = -2, In both cases 1/3y is less than 1.

My question is:
If we plug the fraction 1/9 for Y, we get, 1/3y >1, which renders the first statement insufficient.

Alternatively, if we simplify and rephrase the question like this:
Is y/3 > y^2, and plug 1/10 (or 1/ 9) for Y, we get, Y/3 > y^2. However, for integar values of Y, we get, Y^2 > y/3
Therefore, statement 1 is insufficient.

Please let me know where am I going wrong.
Thanks,

chitrangada:


I absolutely agree..



However,how can you plug a fractional value here, when the question stem specifies x and y to be non zero integers?



How did you arrive at this?You can rephrase the stem as:
xy/x+y>xy
Using Statement 1(x = 2y), we can further reduce it to
2(y^2)/3y>2(y^2) =>Is 1/3y>1? Whatever integer value you substitute will result in a No as an answer. Hence "A" is sufficient.
I Hope you are clear with this...

oops!

Careless mistake.. one of many.

Thanks

:)

_________________
Tim Sanders
Manhattan GMAT Instructor