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 < y < z but x² > y² > z² > 0, which of the following must be positive?

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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:

For positive integers k and n, the k-power remainder of n is defined as r in the following equation:

n = k^w + r, where w is the largest integer such that r is not negative. For instance, the 3-power remainder of 13 is 4, since 13 = 3² + 4. In terms of k and w, what is the largest possible value of r that satisfies the given conditions?

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The following is written by Manhattan Prep College Marketing Associate Kristen Pittard.

New York Cares Day is a day dedicated to service for in-need elementary schools around the five boroughs, where people volunteer their time to renovate schools by painting, restoring playgrounds, organizing libraries, planting flowers, etc.

Last month, a group of Manhattan Preppers made their way to PS 137k, a school that has served the Brooklyn community for over 100 years, to participate in the rejuvenation of the interior by focusing on repainting the main hallway. With rollers and paint brushes in hand and a mint green color picked by the school principal, we were ready to go. After nearly 7 hours of painting, we had transformed an intense red and yellow hallway, into a calming mint green one, just in time for the students to arrive back to school the following Monday. Though we might be better at Data Sufficiency and Reading Comprehension than painting, it was a great experience for our staff to get together on a weekend to give back to the community.

New York Cares Day was a perfect fit for Manhattan Prep due to our core belief in helping students reach their educational goals – and who better to help than the children of New York? If you would like to get involved with any future New York Cares’ projects, they have thousands of projects listed on their website, which range from children’s education to working with the elderly of New York.

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:

Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?

(1) BC is parallel to AD.
(2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.

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On such an auspiciously numbered day, it was disturbing to find an error in this week’s Challenge Problem, XYZ Building. The numbers have now been fixed, so if you’ve already put in an answer, check it out again. We apologize sincerely for goofing up here. Have a great weekend!

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:

In XYZ Building, a flight of stairs connects each floor to the next, and each flight of stairs is separated from the next flight by a landing. Josie takes twice as long to climb a flight of stairs at a constant rate as she does to cross a landing at another constant rate. If it takes Josie 13.3 minutes to climb 7 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 10 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?

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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:

The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4:7:8:12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?

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This article, written by Abby Pelcyger and Stacey Koprince, was adapted from our upcoming book, The GMAT Roadmap: Expert Advice Through Test Day. The full book will be available mid-November.

If you wanted to meet every neighbor on your block, you wouldn’t re-introduce yourself to your best friends who live a few doors down, or to the guy who has you over for a barbeque every fourth Sunday. Rather, you would identify which neighbors you don’t know, and go knock on their doors. The same is true for learning GMAT content. If you are already solid on a bunch of content, reading a whole book on stuff you already know and doing practice problems you could do blindfolded with your hands tied behind your back won’t improve your score. You need to identify the content that you do not yet know, or are still shaky on, and concentrate your efforts there.

The Strategy Guides are written to provide comprehensive coverage of GMAT-level content. It is your job to ascertain how to most effectively use the guides. Here’s what we recommend:

• If you know that you don’t know the content covered in a Strategy Guide chapter, are shaky and/or rusty on the material, or feel that there must be a faster way than how you currently approach the subject, read the chapter. Create a cheat sheet for the chapter by taking notes on key points that you want to remember, but don’t yet have memorized. Then, test your learning by completing all of the In Action problems at the end of the chapter. Make sure to check your answer and review the solution after completing each problem”not after completing the whole set. There is no better way to internalize how not to do something correctly than to repeat an incorrect method fifteen times in a row!

• If you know that you know the content covered in a Strategy Guide chapter, quiz yourself to prove it! Turn to the In Action problems at the end of the chap¬ter. They are listed from easiest to hardest, so try numbers 3 and 8. If you do not get those problems right, read the chapter. If you do get those problems right, complete numbers 11“15. Make sure to check the answers after completing each problem. If you get them all right, move on to the next chapter. If you get them mostly right, skim the chapter and focus in on the pieces of information that you need to fill the holes in your knowledge.

• If the Strategy Guide leaves you confused, it is likely that you have holes in the foundational knowledge on which the GMAT content is built. While reading the Strategy Guide, refer back to the appropriate chapters of the Foundations books, as needed, to fill in these gaps.

In September, GMAC held a Summit for the benefit of the test prep crowd “ all of us, basically. We’ve talked already about a lot of the information that came out of that conference, and we’ve got one last topic for you today: the Next Generation GMAT. As many of you have heard, the GMAT is changing in June of 2012.

The below quotes are all from GMAC or Dr. Lawrence Rudner (Chief Psychometrician, GMAC) and all quotes are copyright 2011 Graduate Management Admissions Council. The headers below are the names of the individual articles from which the information and quotes came.

How is the GMAT changing?

Currently, the GMAT consists of two essays scored on a 0 to 6 scale, a quantitative section and a verbal section, each scored on a 1 to 51 scale, and a total combined score for the quant and verbal sections scored on a 200 to 800 scale.

The new test will drop the Analysis of an Issue essay but keep the Analysis of an Argument essay, scored on the same scale. The quant and verbal sections and scoring, as well as the total score, will also remain the same. A new 30-minute Integrated Reasoning section will be added and it will have its own separate scoring scale; we don’t currently have information about this because they are still in the final stages of determining the scoring system. GMAC has said it expects to release the IR scoring scale in April of 2012.

Initially, test takers will continue to receive quant and verbal scores immediately (at the test center) and the Integrated Reasoning score will be available approximately 20 days later. Eventually, we expect that the IR score will also be available immediately after the test.

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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:

The difference between positive two-digit integer A and the smaller two-digit integer B is twice A‘s units digit. What is the hundreds digit of the product of A and B?

(1) The tens digit of A is prime.

(2) Ten is not divisible by the tens digit of A.

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