Is 0 positive?

[MulaloR302]

Dear GMAT instructor,

I got a little bit confused while working through this GMAT problem using your explanation. I thought 0 is even, but is neither positive nor negative. Please help clarify. I only tested using 0.5 for both and not 0 and 1.

x, y = positive, and x + y = 1

100x + 200y could be = ?

Benchmark Method

The extreme values of x and y occur when either value gets infinitely close to zero. At that same time, the value of the other variable would be infinitely close to one. So imagine the edge of those extremes, where neither x nor y are technically allowed to go: zero and one.

When x = 0 and y = 1:

100x + 200y = 100(0) + 200(1) = 200

When x = 1 and y = 0:

100x + 200y = 100(1) + 200(0) = 100

The actual value of 100x + 200y must therefore be between these values. If you aren’t certain, test a middle value of x and y to see where it falls:

When x = 0.5 and y = 0.5:

100x + 200y = 100(0.5) + 200(0.5) = 150

Therefore only statements II and III could be true. The correct answer is (E).


Kind regards,
Mulalo

[Sage Pearce-Higgins]

Please check the forum guidelines before posting - unfortunately we're not allowed to post Official Guide problems, as they're copyrighted. In future, please take such questions to your course teacher.

You seem to have got a handle on the 'Benchmark Method' - this is just a variant of trying out cases with real numbers to understand what the heck is going on. Your case of 0.5 for both is a good case, but it's not the only one. You're also right in stating that 0 is not a positive number, so, yes, x cannot be 0.

However, when we're testing cases it's a good idea to be "extreme" and to think "what's the biggest or smallest x could be?". Sure, x cannot equal 0, but it can get pretty close, and testing the case in which x = 0.001 and y = 0.999 is going to be pretty tough with the arithmetic. So it's okay to test x = 0, so long as we remember that "x can be close to 0, but a tiny bit bigger than 0". Consequently, 100x can be close to zero, but a tiny bit bigger.