If yz not equal to zero is 0 < y < 1?

To be honest, I'm a huge fan of DS so forgive me in advance for being too giddy ! :p

So let's get cracking !

Let's start by understanding the problem : We're told that y*z is not equal to zero. This should automatically give you the following information : neither y nor z are equal to 0 !!. Then we're asked to answer by yes or no (consider the question stem : "Is... ?") whether \(0<y<1\)

Put your answer choice grid up : (Something I've inherited from MGMAT prep)

AD (I chose to start with statement 1)
BCE

Statement 1 : \(y <\frac{1}{y}\)

Since y isn't equal to 0, the inequality is sound. However since we don't know the sign of y (whether y is positive or negative) we can't multiply each side of the inequality by y since there's the risk that the inequality is flipped. So statement 1 is insufficient.

The grid should look like this by now :

AD
BCE

Statement 2 : \(y = z^2\)

The only information we can gather from this statement is that y is positive. This will be particularily useful when we'll combine both statements. But up to this point, statement 2 is insufficient.

Our grid should look like this :

AD
BCE

Let's combine statements 1 and 2.

From statement 2, we know that y is positive. Therefore, we can multiply the inequality in statement 1 by y without risking to have the inequality flipped. From statement 1 we have, \(y^2<1\). Applying the square root to this inequality yields \(y<1\).

Therefore, we can clearly say that \(0<y<1\). So the final answer is C ! (Oh and don't forget to cross off the E in your grid as well ).

Hope that helped