Page 77 (Chapter 4) 2nd edition-guide 4

[Shulamitj1]

Page 77 (Chapter 4) 2nd edition-guide 4:

15) -x / ((-y)(-z)) , given that xyz > 0

This is going to sound like a stupid question, but I guess I will show my work for what I did.

I changed it to -x/((y)(z)) Then I said it cannot be determined. This study guide said that if you have a '-x' for example, it can be positive, because say x= -5, then -x = 5. So I thought it cannot be determined because you do not know what is positive or negative.

The answer on page 80 is negative; this answer makes sense if we take -x to be a negative number and y and z to be positive ones. Why is it that way here, though?

[tommywallach]

Hey Shula,

The thing to remember on all GRE quant questions is that your answer needs to make use of all the given information. Your explanation seems to more or less ignore the second given xyz > 0. What does that tell us? One of two things. Either:

a) x, y, and z are all positive

OR

b) two of them are positive, and one is negative.

Now look at your equation: -x/yz

Let's consider both possibilities:

a) -(pos)/(pos * pos)

The denominator will be positive and the numerator will be negative, so the whole thing will be negative.

b) This one is a little more complicated. Let's look at both possibilities of two of the three variables being negative (either the numerator and one of the denominators, or both denominators):

-(pos)/ (neg * neg) --> the denominator will be positive and the numerator will be negative, so the whole thing will be negative

-(neg)/ (pos * neg) --> the numerator will be positive and the denominator will be negative, so the whole thing will be negative


As you can see, in all possible situations, the whole expression will be negative. Make sure to use all the givens!

-t