In the figure above, the circle with center O is inscribed inside squa

Question

https://gmatclub.com/forum/download/file.php?id=28835 In the figure above, the circle with center O is inscribed inside square ABCD as shown. What is the ratio of the area of circle O to the area of square ABCD ? A. \frac{\pi}{2} B. \frac{4}{\pi} C. \frac{\pi}{3} D. \frac{\pi}{4} E. \frac{\pi}{5} 2016-01-04_0003.png

peachfuzz · Answer

What is the ratio of the area of circle O to the area of square ABCD ?

let r=1
let side of square = 2

pi*r^2 / 2^2
=pi/2

A.  \frac{\pi}{2}

anurag790 · Answer

ans is pi/4
Side of the square= diameter of the circle 
Area of square = 4 r^2 
Area of circle= pi r^2 
Ratio= pi/4

davedekoos · Answer

The question asks for the Area of circle / Area of square
The side of the square is the diameter of the circle = 2r
So the ratio of the areas is:

\frac{πr^2}{(2r)^2}

\frac{πr^2}{4r^2}

\frac{π}{4}

Answer: D

Kelzie01 · Answer

Is test it safe for this question? If each side = 4, the equation is pi(2^2)/(4^2) -> 4pi/16 -> pi/4

Clearly it worked, but will it always?

davedekoos · Answer

Yes, it will work for no matter what number you choose. The key here is that the diameter of the circle is equal to the side of the square. If you notice in the algebraic solution above, the r term disappears; that means that the solution is independent of the value of r.

In general, picking numbers will get you to the solution, as long as you pick valid numbers. In the case of this problem, that's easy, any positive number will work. (negative numbers would work too, but it just doesn't make sense to pick a negative length). In other problems, picking valid numbers might not be as straightforward as one would like. Choosing a strategy for each specific problem that allows the quickest and easiest solution is always the best approach.

Cheers,

EMPOWERgmatRichC · Answer

Hi peachfuzz,

Your approach to TEST R=1 was perfect, but you made a small error in your calculation. It should be...

pi*r^2 / 2^2 =
pi(1)^2/4 = 
pi/4

As you continue to practice, you have to be VERY careful about the little details. In certain questions, one or more of the wrong answers will be the result of a mistake that a Test Taker MIGHT make - so you won't even realize that you've made that mistake.

GMAT assassins aren't born, they're made,
Rich

bumpbot · Answer

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In the figure above, the circle with center O is inscribed inside squa

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