Is the area of the circle with center O larger than the area of the

Question

https://gmatclub.com/forum/download/file.php?id=38120 Is the area of the circle with center O larger than the area of the region outside the circle and inside the square ABCD ? The straight line OEF is parallel to AB. (1) OE < AB/4 (2) EF < AB/4 2017-10-22_1751.png

Hannah2424 · Answer

Official answer from Barron's GMAT:

The area of the circle plus the area of the region outside of the circle and inside of the square is equal to the area of the square, which is (AB)^2. Thus, if you can determine whether one are is larger (or smaller) than .5(AB)^2, that is sufficient.

Statement 1 alone is sufficient since the area of the circle is (pi)(OE)^2, and if (1) holds, then (pi)(OE)^2<(pi)((.25)(AB))^2. But since pi/16 is less than ½, we can answer the question. So the answer to question 1 is YES, and the only possible choices are A or D.

Statement 2 alone is not sufficient snce (2) does not give any information about the radius of the circle. Note you might think OE+EF=.5*AB; however, that requires the additional information that O is also the center of the square, which is NOT give.

Correct choice is A

Mick1005 · Answer

Since OE is the radius of the circle statement (1) gives information about the radius which is 1/4th of the side of the circle. Thus we can conclusively say that the area of the circle with center O is less than the area of the region outside the circle and inside the square ABCD.
Statement (2) Gives info about EF which does not prove anything.
My Pick:A

delid · Answer

Hi everyone, I can't really understand why statement 1 is sufficient. Could someone try to explain their logic?
Thanks a lot for the support!

Mick1005 · Answer

Hi delid.

Statement (1) gives Info about OE i.e radius of the circle.
Oe<AB/4. Let AB=8
=> OE<8/4
=>OE<2.(Let say 1.999999 i.e approximately 2)
=> Area of the Circle = Pi*r*r= 3.14* 2*2=12.56
Area of square=8*8=64.
Thus we can answer the question since we have both area of circle and square.
Hence. A.

Is the area of the circle with center O larger than the area of the

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Is the area of the circle with center O larger than the area of the

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