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:

Triangle ABC is cut by a line DE parallel to side AC, as shown in the diagram. If side AC has length 1, and the area and perimeter of triangle ABC are both twice the corresponding values for trapezoid ADEC, what is the perimeter of triangle DBE?

Read more

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:

Each of seven consecutive integers, all greater than positive integer n, is divided by n. The seven resulting remainders, not necessarily distinct, are assembled into a list L. What is the value of n?

(1) List L contains two odd values and 5 even values.

(2) No odd integer appears in list L more than once.

Read more

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:

An insect is located at one corner (point A) on the surface of a rectangular solid that measures 3 x 4 x 5 inches, as shown in the diagram.

 

Note: Figure is not drawn to scale.

If the insect crawls along the surface of the rectangular solid to the opposite corner (point B), what is the shortest possible length, in inches, of the insect’s path from point A to point B?

Read more

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 trapezoid above, with sides a, b, c, and 1, what is the value of ac ?

(1) a + c = b

(2) a “ c = 1

Read more

A few months ago, I wrote a couple of articles targeted toward those students looking for a super-high score (one for quant, one for verbal). I challenged students to answer those questions in much less time than we typically average on test questions.

Well, I’m back with another one in the series. This problem is a bit different though: it’s from our Challenge Problem archive, a question bank consisting of what we call 800+ level problems. (Some might qualify as 750+ but most are harder than anything you’ll ever see on the real test.)

Do you need to be able to answer a question like this in order to score 750+? Absolutely not. (In fact, after my colleague Ron Purewal submitted this question, I tested it out on several of my fellow instructors, all of whom have scored 760+ on the test. Not everyone answered correctly.) Mostly, I’m offering this to stretch your brains, drive you a little crazy, and make one important point (see my second takeaway at the end).

If, however, quant is your strength and you’re hoping to score 51 in that section”you can certainly score 51 without getting this one right, but if you do get this one right in 2 minutes, then you know you’re ready for the quant section.

One more tidbit before we dive in. I chose this question because it is SO very hard. As of right now (as I’m typing this), 254 people have tried this problem and 44 have answered it correctly.

Do a little math here. What percentage of people answered the question correctly?

17%. Random guess position is 20%. Wow.

Read more

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 octagon in the diagram above is regular: all of its sides are of equal length, and all of its angles are of equal measure. If the octagon’s perimeter is 8 inches, and every other vertex of the octagon is connected to create a square as shown above, what is the area of the square?

Read more

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 5a + 7b = k, where a and b are positive integers, what is the largest possible value of k for which exactly one pair of integers (a, b) makes the equation true?

Read more

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 length and width of a rectangle are integer values. What is the area of the smallest such rectangle that can be inscribed in a circle whose radius is also an integer?

Read more

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 a certain type of tiling called Penrose P3 tiling, two types of rhombi fill a space without gaps or overlaps: wide rhombi and narrow rhombi. If five of the wide rhombi can meet symmetrically at a single point, while ten of the narrow rhombi can, what is the ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus?

Read more

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, what is the value of |x “ 3| “ 2|x “ 4| + 2|x “ 6| “ |x “ 7| ?

(1) x is an odd integer.

(2) x > 6

Read more