Articles published in Challenge Problem

Challenge Problem Showdown- April 1, 2013

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challenge problem
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 of a to b is twice the ratio of b to c.  If ab, and c are positive integers, which of the following statements cannot be true?

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Challenge Problem Showdown – March 25, 2013

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challenge problem
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:

Which of the following cannot be the sum of two or more consecutive positive integers?

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Challenge Problem Showdown – March 11, 2013

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challenge problem
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 the expression b, the $ symbol represents one of the following arithmetic operations on a and b (in the order the variables are shown): addition, subtraction, multiplication, and division. Given that it is not true that a $ b = b $ a for all possible values of a and b, a pair of nonzero, non-identical values for a and b is chosen such that a $ b produces the same result, no matter which of the operations (under the given constraints) that $ represents. The nonzero value of b that cannot be chosen, no matter the value of a, is

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Challenge Problem Showdown – March 4, 2013

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challenge problem
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:

At noon, Adam begins painting a house. Two hours later, Clara begins painting the same house and one hour after that, Wong begins painting the house. Each works without stopping at his or her respective constant rate. In the end, each paints 1/3 of the house. Working together and starting at the same time, Adam and Wong could paint the entire house in half the time it would take Clara to paint the house by herself. How long would it take Adam to paint the house entirely by himself?

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Challenge Problem Showdown – Feb 25, 2013

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challenge problem
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 x3.5 > y2.5 > z1.5, then which of the following cannot be true?

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Challenge Problem Showdown – Feb 11, 2013

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challenge problem
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:

How many integer values of x satisfy the relationship x4 “ 4x3 “ 4x2 +16x ≤ 0?

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Challenge Problem Showdown- Feb 11, 2013

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challenge problem
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:

A regular octagon (a polygon with 8 sides of identical length and 8 identical interior angles) is constructed. Next, an equilateral triangle (with sides identical in length to those of the octagon) is attached to each side of the octagon, such that each side of the octagon coincides exactly with the side of the triangle. Finally, each triangle is folded over that coincident side onto the octagon, covering part of the latter’s area. Approximately what proportion of the area of the octagon is left uncovered?

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Challenge Problem Showdown- Feb 4, 2013

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challenge problem
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:

Is xy an integer?

(1) x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square.

(2) y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.

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Challenge Problem Showdown- Jan 28, 2013

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challenge problem
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:

A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability of generating an odd prime digit is between

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Challenge Problem Showdown- Jan 21, 2013

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challenge problem
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 a prime number, the function G(x) is defined as the xth root of the product of all distinct primes less than or equal to x. If x is one of the first five primes, the maximum value of G(x) occurs when x =

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