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:

The country of Sinistrograde uses standard digits but writes its numbers from right to left, so that place values are reversed. For instance, 12 means “twenty-one.” A five-digit code from Sinistrograde is accidentally interpreted from left to right. If all possible five-digit codes (including zeroes in all positions) are equally likely, what is the probability that the code is in fact interpreted correctly?

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Today we’re going to talk about statistics problems in which we have to combine knowledge of more than oneconcept.Try this GMATPrep® problem first; set your timer for 2 minutes and go!

“Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

“I. At least one of the homes was sold for more than $165,000.

“II. At least one of the homes was sold for more than 130,000 and less than 150,000.

“III. At least one of the homes was sold for less than $130,000.

“(A) I only

“(B) II only

“(C) III only

“(D) I and II

“(E) I and III”

Sigh. I hate roman numeral questions. I have to do more work to solve the problem, and I never like that. : )

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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:

If x is positive and not equal to 1, then the product of x^1/n for all positive integers n such that 21 ≤ n ≤ 30 is between

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Modifiers have always been commonly tested on the GMAT and emphasis on meaning has increased recently. In addition, these two areas can often be quite tricky – it’s hard to articulate exactly what the issues are sometimes. So let’s try talking one through. This problem is from GMATPrep®. Set your timer for 1 minute 15 seconds and go for it!

*  “Initiated five centuries after Europeans arrived in the New World on Columbus Day 1992, Project SETI pledged a $100 million investment in the search for extraterrestrial intelligence.”

“(A) Initiated five centuries after Europeans arrived in the New World on Columbus Day 1992, Project SETI pledged a $100 million investment in the search for extraterrestrial intelligence.

“(B) Initiated on Columbus Day 1992, five centuries after Europeans arrived in the New World, a $100 million investment in the search for extraterrestrial intelligence was pledged by Project SETI.

“(C) Initiated on Columbus Day 1992, five centuries after Europeans arrived in the New World, Project SETI pledged a $100 million investment in the search for extraterrestrial intelligence.

“(D) Pledging a $100 million investment in the search for extraterrestrial intelligence, the initiation of Project SETI five centuries after Europeans arrived in the New World on Columbus Day 1992.

“(E) Pledging a $100 million investment in the search for extraterrestrial intelligence five centuries after Europeans arrived in the New World, on Columbus Day 1992, the initiation of Project SETI took place.”

As we discuss this problem, I really want you to think about how to articulate why something is incorrect (or correct). Pretend you’re the teacher and you have to explain it to your students. Also, I’m going to give us a bit of a handicap. You aren’t allowed to use this reason: It changes the original meaning of the sentence.

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We are excited to announce that we are now accepting applications for our Winter 2012 Social Venture Scholars (SVS) program. For those unfamiliar with the program, it was launched in 2007 with the goal of making GMAT prep more accessible to MBA-hopefuls working in the non-profit sector. The very first SVS class was taught by our founder, Zeke Vanderhoek. Over the past 5 years we have run 6 SVS programs and helped dozens of deserving individuals get a step closer to business school. Past SVS students have gone on to gain admission to competitive business schools (such as Columbia and Duke), and have used their degrees to advance and found organizations dedicated to positive social change.

Recipients of our SVS scholarship receive free enrollment into a dedicated Live Online GMAT prep course (a $1090 value). Up to 25 scholarships will be awarded to applicants who (1) currently work full-time in an organization that promotes positive social change, (2) plan to use their MBA to work in a public, not-for-profit, or other venture with a social-change oriented mission, and (3) demonstrate clear financial need. This year’s SVS course will begin on Monday, February 20th.

For complete details and application requirements, visit our Social Venture Scholars page. Applications for the Winter 2012 program are due on February 1st. Good luck!