If yx cannot equal 0, is 0<Y<1?

y< 1/y

Sub Y=0.5

0.5<1/0.5 - true

Here we can conclude that Y lies between 0 and 1.

Similarly Sub Y= -2

-2< -1/2 - which is again true.

Here we can conclude that Y doesn't lie between 0 and 1.

Hence the statement contradicts each other.

So it isn't sufficient.

Wow, that was really relatively simple. Not quite sure what I was thinking last night. I could have just substituted -2 -1 -.5 0 .5 1 2 in and figured it out. Thank you for the response sir.

-BP

ceilidh.erickson : Thanks for your valuable advice.. And it's indeed true that one got to be very precise while reasoning a GMAT question, not only for the sake of others but also for self.. Point taken.. Thanks again..

If yz does not equal zero. Is 0<y<1?
(1)y<1/y
(2)y=z²

The solution below offers a slightly different way to reason through statement 1.

Statement 1: y < 1/y.
The CRITICAL POINTS are where y = 1/y or where the inequality is undefined.
y = 1/y when y=1 or y=-1.
y < 1/y is undefined when y=0.
When y is ANY OTHER VALUE, y < 1/y or y > 1/y.
Thus, there are 4 ranges to consider: y < -1, -1<y<0, 0<y<1, and y>1.

To determine the range of y, test one value to the left and right of each critical point.
If y = -2, then the inequality becomes -2 < -1/2.
This works. Thus, y<-1 is part of the range.

If y = -1/2, then the inequality becomes -1/2 < -2.
Doesn't work. Thus, -1<y<0 is not part of the range.

If y = 1/2, then the inequality becomes 1/2 < 2.
This works. Thus, 0<y<1 is part of the range.

If y = 2, then the inequality becomes 2 < 1/2.
Doesn't work. Thus, y>1 is not part of the range.

Thus, it's possible that y<-1 or that 0<y<1.
INSUFFICIENT.

Statement 2: y=z².
Since the square of a number cannot be negative, and it is given that yz≠0, we know that y>0.
Thus, it's possible that y=1/2 (in which case 0<y<1) or that y=2 (in which case y>1).
INSUFFICIENT.

Statements 1 and 2 combined:
The only range that satisfies both statements is 0<y<1.
SUFFICIENT.

The correct answer is C.

An algebraic way to determine the CRITICAL POINTS of y<1/y is to multiply each side by y².
We can safely multiply by y² for the following reasons:
y≠0, since 1/y is undefined when y=0.
y² cannot be negative, since the square of a value cannot be negative.
Thus, y²>0.
The result is that we can safely multiply each side by y², knowing that the direction of the inequality will not change:

y²(y) < y²(1/y)
y³ < y
y³ - y < 0
y(y² - 1) < 0
y(y+1)(y-1) < 0.

The CRITICAL POINTS are where y(y+1)((y-1) = 0:
y=-1, y=0 and y=1.