Source: Official Guide Revised GRE 2nd Ed. Part 9; Section 6; #6

9

# (x + 3)(y - 4) = 0

(x + 3)(y - 4) = 0 Quantity A : xy Quantity B : -12 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

### 4 Explanations

1

Alyssa L

Question. Is it x=-3 OR y=4 because x and y are different variables? What if the equation was (x+3)(x-4)=0?

Nov 30, 2020 • Comment

Hi Alyssa,
Even if the variables were the same, we would have x = -3 OR x = 4. Either one works, so we don't know which one is actually true. There are two possible values for x there.

1

Hello Chris,
Can we instead reason that there are two variables and one equation so there are infinite number of solutions and hence not necessarily equal to -12? Thanks!

Jan 3, 2014 • Comment

Lucas Fink

That's good to notice, but we're not trying to find the exact values of x and y, so it doesn't mean anything certain. We're only trying to find whether xy is greater than, equal to, or less than 12. That's much less specific information--it's possible that several different values of x and y would multiply together to a product greater than quantity B.

In short, two variables and one equation only means you can't find the exact values of those two variables. It doesn't mean you can't extract other information.

Of course, as explained below, with this question, there's an entirely different route we should take which does lead us to "cannot be determined" anyway, so pay close attention to that. If you see (x + 3)(y - 4) = 0, or any such similar equation, you should immediately recognize that (x+3)=0 or (y-4)=0. That's the key.

2

Zhao Zhai

the answer should be D. the result is x=-3 or y=4. it is not x=-3 and y=4. As a result, the relationship cannot be determined.

Jun 4, 2013 • Comment

Chris Lele

You're absolutely right about this, Zhao, so thank you for pointing that out! The explanation video to this question has an error, so please disregard it until I can replace it. I'm sorry about the confusion, and in the mean time, here's the correct solution:

Either x=-3, y=4, OR both are true. We do not know that x=-3 AND y=4, so we can't find xy.

To illustrate, it's possible that x=-3 and y=10, in which quantity B would be greater, and it's possible that x=10 and y=4, in which case quantity A would be greater.

Thanks again, and sorry about that!

4

Chris Lele

Dec 8, 2012 • Comment