mGRE practice question

[vlad4]

Hello,

I just got a question in my mGRE (Test 5) that asked to calculate the following:

"In the figure above, a 100-meter long circular running track is inscribed inside of a square field. Approximately what fraction of the square field is enclosed within the circular track?"

The Manhattan GRE provides a very long answer that actually uses the "100" to calculate the areas of the circle and square.

Wouldn't be just easier to do the following?

(Pi*r^2)/(2r)^2 => Pi/4 => 78%

Or am I missing some fundamental concept/rule, which says that I cannot skip using the length provided?

Thanks

[navigalactus]

"In the figure above, a 100-meter long circular running track is inscribed inside of a square field. Approximately what fraction of the square field is enclosed within the circular track?"

Where's the figure?

Anyways as per your question, there is no harm in doing this as you're solving this entirely using variables that are correctly co-related. Left over was calculated correctly to be 78.53%

You are not missing anything

[tommywallach]

Hey Guys,

That's absolutely right. The reason why we don't do it that way is that it doesn't necessarily occur to everyone that an inscribed circle will always take up the same proportion of space in the square. That's a great insight, but we want to make sure a student would be comfortable doing the math here just to prove it for certain.

All that being said, you're absolutely right that you can make that assumption, and so solve without using the numbers.

-t

P.S. Technically, you're plugging in 1 for the radius... : )