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 :
ADBCE
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 :
ADBCE
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