DS: If x and y are nonzero integers...

[thatsku]

Taken from the MGMAT EIV question bank:


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


The answer rephrases the question as follows:

Is (1/x + 1/y)^-1 > (1/x * 1/y)^-1 ?
Is [(x+y)/xy]^-1 > [1/xy]^-1 ?

then the answer takes the reciprocal of both sides

Is xy/(x+y) > xy ?

My question is: how can you safely take the reciprocal and rephrase if you don't know the sign of xy or (x+y)? The prompt only indicates that x and y are non-zero integers but says nothing about signs.

Thanks in advance!

[RonPurewal]

take a look at this again:

Is [(x+y)/xy]^-1 > [1/xy]^-1 ?

then the answer takes the reciprocal of both sides

Is xy/(x+y) > xy ?

My question is: how can you safely take the reciprocal ...

no such thing has been done, actually; those equations are EXACTLY the same.

if the first equation had just been "(x + y)/xy > 1/xy" -- i.e., WITHOUT the -1 powers on both sides -- THEN you would actually have to "take the reciprocal".
but, since the -1 powers are already there, you're not actually transforming the equation; you're just executing the powers that are already indicated by the exponents in the problem.

[yousuf_azim]

Dears,

What is the ans?

[jnelson0612]

Dears,

What is the ans?

The answer is A.