### 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, ABC is a right triangle with AC as its hypotenuse, and PQRS is a square. What is the area of the square?

(1) AC is 70 units long.

(2) The product of the length of AS and the length of RC is 396.

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The weekly winner, drawn from among all the correct submissions, will receive One Year of Access to our Challenge Problem Archive, AND the GMAT Navigator, AND Our Six Computer Adaptive Tests (\$92 value).

1. mkuma36 August 19, 2013 at 12:13 pm

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.