We invite you to test your GMAT knowledge for a chance to win! The second week of every month, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that month’s drawing for free Manhattan GMAT prep materials. Tell your friends to get out their scrap paper and start solving!

Here is this month’s problem:

If p, q, and r are different positive integers such that p + q + r = 6, what is the value of x ?

(1) The average of x^p and x^q is x^r.

(2) The average of x^p and x^r is not x^q.

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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:

Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is

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