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Manhattan GMAT Challenge Problem of the Week – 7 Sept 2010

by Manhattan Prep, Sep 7, 2010

Here is a new Challenge Problem! If you want to win prizes, try entering our Challenge Problem Showdown. The more people enter our challenge, the better the prizes.

As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!

Question

It takes Abby a hours to build a birdhouse. When Becky and Caroline help Abby, the three of them can build an identical birdhouse in half the time. If it takes Becky and Caroline b and c hours, respectively, to build a birdhouse on their own, which of the following statements is true?

(A)

(B)

(C)

(D)

(E)

Answer

The key to this problem is the second sentence. When Becky and Caroline help, the time it takes to build the birdhouse is cut in half. That means that Becky and Caroline, when working together, work at a rate equal to the rate Abby works at.

We can represent the rates that Abby, Becky and Caroline work as 1/a, 1/b and 1/c, respectively. Therefore:

All of the answer choices have an expression equal to 0, so combine fractions and move them all to the left side of the equation. The common denominator for all fractions is abc.

The correct answer is C.

Special Announcement: If you want to win prizes for answering our Challenge Problems, try entering our Challenge Problem Showdown. Each week, we draw a winner from all the correct answers. The winner receives a number of our our Strategy Guides. The more people enter, the better the prize. Provided the winner gives consent, we will post his or her name on our Facebook page.

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