GPREP #19

[hardikrs]

if x <> -y, is (x-y)/(x+y) > 1

1. x > 0
2. y < 0

using the given equation (x-y)/(x+y) > 1 ,cant we write x-y > x+y, so 2y <0, so y<0 so 2 is suff. But OA is E.

Please explain your answer.

Thanks,

[eravi11]

no u can't write (x-y)/(x+y) > 1 as x-y > x+y because we dont know the sign of x+y. only if x+y would have been positive, we can multiply the terms in inequality..

to solve this..write the term as (1 - y/x)/(1+y/x) >1
we know individually statements are insufficient.
Combining 1 and 2, i.e. x>0 and y<0

we know Numerator term 1-y/x will always be postive and >1 but 1+y/x could be positive or negative depending on the value of x and y. Thus E.

For e.g for x=2, y= -3, 1+y/x is negative.
for x=2 and y= -1, 1+y/x is positive.

[abhasjha]

Inequalities changes their sign if multiplied by negative .If (x+y ) is a negative number then

(x-y)/(x+y) > 1

when cross multiplied becomes (x-y) < x+y ..... beware of this trap which GMAT uses often ........... If you dont know then sign of the variable simply dont multiply .....