by **cgentry** Sat Oct 22, 2016 9:40 pm

Huh. This is an interesting issue.

We need to keep in mind that "r" is a numerical value for yards, and that number exists independently of the units. The units only come into play when we try to convert between units.

So the question should really be

is 3.14*r^2 square yards >= r square yards? The unit exists only in that we are working with numerical values for area. If you have a science background (my undergrad degree is chemical engineering), this is probably a little bit irritating. I was always taught to track my units. But keep in mind that was for real-life applications. And while the GMAT allows real-life assumptions (more on that in a moment), GMAT problems are not meant to exactly mimic a real-life mathematical issue.

So in this case, if you're tracking units, both units would cancel. So then the question becomes "is 3.14 r^2 >= r?"

So here we get to the real life assumptions the GMAT will allow. We don't deal with negative dimensions. And also, since the problem states that the circle exists, r =/= 0.

So we can divide both sides of this inequality by r, and get

is 3.14 r >= 1?

And you can divide both sides by 3.14, to get

is r >=1/3.14 ?

Notice that I haven't done any unit conversions yet. Now, when we get to the idea of unit conversions, we need to put the units back into the question. Essentially, we're asking if the radius is greater than 1/3 of a yard.