GMAT Challenge Problem Showdown: August 19, 2013

Lauren Golin —  August 19, 2013 — 1 Comment

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.

GMAT Challenge ProblemTo see the answer choices, and to submit your answer, visit our Challenge Problem Showdown page on our site.

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Lauren Golin

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One response to GMAT Challenge Problem Showdown: August 19, 2013

  1. 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.

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