GMAT Challenge Problem Showdown: August 19, 2013


challenge problem
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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  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.