GMAT Official Guide 12: PS #148

Zeke– is there any possible way of going about this problem without having to simplify and then find the boundaries of x and y? The explanation in the OG12 is very confusing. I wanted to know if there was a more efficient way to solve this problem.

Thanks!
Katie

Hi Katie,

The question implies that there are certain values that k cannot be. Indeed, the OG explanation is confusing. Most people would not be able to simplify expressions to that level of depth.

But because you know that k cannot be certain values, you can always try the various values of x, y, and k. Put together a chart and do some quick math in your head. Make sure you write it out and that you only test values of x

You can simplify it up to the expression 10y/(x+y)..then put the following table together

x y expression (10y/(x+y)
———————
1 2 6.7ish
1 3 7.5
2 3 6
2 8 8
2 20 ~10

So it seems like we found values of k in the range of 6-10ish is doable. You need to add 10 to it since the expression you simplified it to was

10 + 10y/(x+y)

So the range of k values is roughly 16-20. Of the answer choices, only 18 fits in (D). And you can assume that the reason why you haven’t been able to generate values outside of that range is because those are invalid values of k. So you can safely assume all the other answer choices are no good.

Hope that helps!

GMAT Pill Support Team

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