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:

For all positive integers n and m, the function A(n) equals the following product:

(1 + 1/2 + 1/2²)(1 + 1/3 + 1/3²)(1 + 1/5 + 1/5²)…(1 + 1/p_n + 1/p_n²), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is

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

Discuss this week’s problem with like-minded GMAT takers on our Facebook page.

The weekly winner, drawn from among all the correct submissions, will receive One Year of Access to our Challenge Problem Archive, AND the OG Archer, AND Our Six Computer Adaptive Tests ($92 value).

Other Posts You May Like:

• Challenge Problem Showdown – February 26th, 2012
• Challenge Problem Showdown – February 13th, 2012
• Challenge Problem Showdown – May 14th, 2012