Each week, we 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 two free Manhattan Prep GRE Strategy Guides.

Joseph has 8 friends. Some of these 8 friends know each other, as follows: Mary knows Dave and Edgar, who also know each other. Edgar, in addition to knowing Mary, knows Lea, Juan, and Greg, none of whom know each other. If Joseph would like to introduce each of his friends to all of his other friends whom that friend does not already know, how many introductions will Joseph have to make?

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Each week, we 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 two free Manhattan Prep GRE Strategy Guides.

An online bank verifies customers’ ownership of external bank accounts by making both a small deposit and a small debit from each customer’s external account, and asking the customer to verify the amounts. In 70% of these exchanges, the deposit and debit are within two cents of one another (for example, a deposit of $0.18 and a debit of $0.16, or a deposit of $0.37 and a debit of $0.38), and the deposit and debit are always within five cents of one another. During one week, the online bank attempts to verify 6,000 accounts in this manner, but 0.5% of the transactions do not go through, and thus no money is transferred. What is the maximum amount, in dollars, that the account verification system could have cost the bank that week?

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Each week, we 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 two free Manhattan Prep GRE Strategy Guides.

Peopletown’s population increased by x% in 2008 and by 2x% in 2009, where x is a positive integer. By what percent, in terms of x, must the population have decreased in 2010 if the population at the end of 2010 was equal to the population at the end of 2007?

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Each week, we 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 two free Manhattan Prep GRE Strategy Guides.

In the figure above, a circle is inscribed in a triangle.

Quantity A
The shaded area

Quantity B
The area of the circle

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Thank you to all who caught our mistake, now corrected, on “Yippee!”, our Math Beast problem for the week of 10/17/11. As the posted explanation revealed, both Quantities were intended to have a factorial in both numerator and denominator. However, the posted question was missing that crucial exclamation point in the numerator of Quantity B, an omission that affected the answer. The error occurred for the most mundane of reasons: fancy fractions and figures must be created separately and posted as image files, not a simple cut-and-paste. We regret that we lost the “!” during image creation, and apologize for any consternation this may have caused. Thanks for keeping us on our toes! <-- Exclamation point pun intended.

Each week, we 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 two free Manhattan Prep GRE Strategy Guides.

This week’s question is below. Get out their scrap paper and start solving!

{8, 10, 11, 16, 20, 22, 25, x}

In the set above, x is an odd integer between 13 and 21, inclusive. Each possible x value is equally probable.

Which of the following statements has the highest probability of being true?

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