Syed
Hi Bunuel!
How did you so quickly come to this conclusion that "for all other values of 'y' the equation 'x(1-y)/y' will be '-ve'?
Also, how can I strengthen my inequalitites knowledge (for GMAT).
Please explain in detail.
OK, first of all get rid of x, it's positive thus won't affect anything in the case of sign. We have (1-y)/y: even not doing any deep inquires it's obvious that we have an inequality with y and knowing nothing about it, so we can not conclude whether (1-y)/y positive or not. But if we just for practice want to determine when inequality (1-y)/y>0 holds true we can do the following:
We have 1-y and y, thus we have two check points 1 and 0 (check points y-1=0 -->
y=1 and
y=0). We should check three cases for (1-y)/y:
1. y<0 --> denominator y is negative, nominator is positive 1-negative=1+positive=positive, so (1-y)/y negative (positive/negative=negative)
2. 0<y<1 --> denominator y is positive, nominator also positive 1-positive number less than 1=positive, so (1-y)/y positive (positive/positive)
3. y>1 --> denominator y is positive, nominator is negative 1-positive number more than 1=negative, so (1-y)/y negative (negative/positive)
We have that (1-y)/y (and thus x(1-y)/y) is positive when y is in range (0;1) and negative when y<0 or y>1.
So statement (2) gives us two scenarios for x(1-y)/y, hence not sufficient.
Hope now it's clear.