### GMAT Challenge Problem Showdown: August 19, 2013

We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!

Here is this week’s problem:

In the figure above,

ABCis a right triangle withACas its hypotenuse, andPQRSis a square. What is the area of the square?(1)

ACis 70 units long.(2) The product of the length of

ASand the length ofRCis 396.

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Let us consider the side of square be x cm.

Triangle ABC ~ APS [RHS] => x/BC = AS/AB => AS = (AB/BC) * x ——-(1)

Similarly, Triangle QRC ~ ABC [RHS] => x/AB = RC/BC => RC =(BC/AB) * x ——(2)

(1) * (2)

AS * RC = x^2 —–(3)

From the DS statemt (2)

396 = x^2 {which is the area of square} => Therefore sufficient

Hence (B) is the correct answer.