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 three different integers are selected at random from the integers 1 through 8, what is the probability that the three selected integers can be the side lengths of a triangle?

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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:

In the figure above, ABC is a right triangle with AC as its hypotenuse, and PQRS is a square. What is the area of the square?

(1) AC is 70 units long.

(2) The product of the length of AS and the length of RC is 396.

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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 how many unique pairs of nonnegative integers {a, b} is the equation a² – b² = 225 true?

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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:

A coin purse contains 13 coins, each worth 1, 5, 10, or 25 cents; the total value of the coins is 150 cents. How many 10-cent coins are in the purse?

(1) The 13 coins can be divided among five separate envelopes so that each envelope contains the same total monetary value.

(2) The 13 coins can be divided among six separate envelopes so that each envelope contains the same total monetary value.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

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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:

A total of m different points are selected on a particular line, and a total of n different points are selected on another line parallel to the first, where each of m and n is greater than 1. In how many different ways can a triangle be made with its vertices at three of the selected points?

A. m²n + mn²

B. mn(m + n – 2)

C. 

D. 

E. 

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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:

In the xy-coordinate plane, line L passes through the points (b, a) and (c, 0), and line Mpasses through the point (a, b) and the origin, where a, b, and c are different nonzero integers.  Do lines L and M intersect?

(1) 

(2) c < 0

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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 n is a positive integer greater than 1, what is the smallest positive difference between two different factors of n?

(1)  is a positive integer.

(2) n is a multiple of both 11 and 9.

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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 PQ is a diameter of the circle above, and the lengths of AX, BX, PX, and QX are integers, what is the area of the circle?

(1) (AX)(BX) = 16
(2) QX > AB

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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:

You have 1 minute (yes,  only one minute!) to do this problem. Further, don’t do any long-hand math (multiplication, etc.)”shortcuts exist for every single calculation. Find them!

In how many ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?

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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:

A point Q is located within the interior of a square ABCD so that it is 1 unit from vertex A, 2 units from vertex B, and 3 units from vertex D. The measure of angle AQB is

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