Manhattan GMAT Challenge Problem of the Week – 20 Sept 2010

by Manhattan Prep, Sep 21, 2010

Here is a new Challenge Problem! If you want to win prizes, try entering our Challenge Problem Showdown. The more people enter our challenge, the better the prizes.

As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!

Question

A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A) 2 : (2pi)

(B) 1 : 2pi

(C) 2pi : 2

(D) 1 : 2pi

(E) 1 : 2pi

Answer

Real numbers are an excellent strategy in solving this problem. Say the radius of the circle is 1, and therefore its area is pi. Thus, the area of the square is also pi, and its side is, consequently, pi.

Since the diagonal of a square is the same as the hypotenuse of a 45-45-90, the diagonal of the square is now pi times 2 , or (2pi).

Be careful the question asks for the diameter of the circle, which is 2. Thus, the answer is 2 : (2pi).

The answer is A.

If you chose to make up a number for the square, your answer will look somewhat different but will still resolve to 2 : (2pi).

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