Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The first multi-part inequality that we are given, x < y < z, means that on a number line, x is to the left of y, which is to the left of z. There is no information about whether any of these quantities is positive or negative, though.
The second multi-part inequality that we are given, x 2 > y 2 > z2 > 0, means that x is further from 0 than y, which is further from 0 than z (which itself is not 0). In other words, we know that |x| > |y| > |z|, and none of these variables equals 0. Again, we cannot infer anything from this information alone about the signs of the variables.
Finally, putting these two pieces of information together, we can conclude something about the signs of some of the variables. Take x. It is to the left of y, but it is also further from 0 than y. The only way for both of these facts to be true is for x to be negative (that is, to the left of 0 on the number line).
The same argument holds true for y itself, since it is to the left of z but also further from 0 than z. So we know that both x and y are negative.
However, we don’t know anything about the sign of z. It could be positive or negative (it just has to be the closest variable to 0).
Looking at the answer choices for a “must be positive” expression, we can plug in a minus sign (–) for x and y and a +/– for z.
The only positive-definite expression is x3y5z<4, or (–)3(–)5(+/–)4, since this becomes a negative times a negative times a positive.
The correct answer is B.
