### Archives For 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 set of n identical triangles with angle x° and two sides of length 1 is assembled to make a parallelogram (if n is even) or a trapezoid (if n is odd), as shown. Is the perimeter of the parallelogram or trapezoid less than 10?

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 isosceles triangle with one angle of 120° is inscribed in a circle of radius 2. This triangle is rotated 90° about the center of the circle. What is the total area covered by the triangle throughout this movement, from starting point to final resting point?

(A)
(B)
(C)
(D)
(E)

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 is the largest?

(A) 227.3
(B) 318.2
(C) 511.1
(D) 79.1
(E) 115.1

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:

Right triangle ABO is drawn in the xy-plane, with OB as hypotenuse, where O is at the origin and B at (15, 0). What is the area of the triangle?

(1) The x- and y-coordinates of all three points are non-negative integers.

(2) No two sides of the triangle have the same length.

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 diagram above, triangle ABC is equilateral, figure SQRE is a square, and A is the midpoint of SQ. If the perimeter of triangle ABC is 6 inches, what is the length, in inches, of segment RY ?

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 different pairs of integers (ab) exist such that 2 < a < 200 and a + b > ab ?  (Two pairs of numbers are considered different if either a or b differs.  For example, (2, 3) and (2, 4) are considered different, although they don’t satisfy the requirements of this problem.)

We hope everyone had a happy Halloween! Yesterday we asked our friends on our Manhattan GMAT Facebook page to attempt this spooky Halloween Challenge Problem. As promised, today we are sharing the answer and explanation to the problem:

This question is not as complicated as it may initially seem. The trick is to recognize a recurring pattern in the assignment of the ghouls.

First, we have five ghouls (let’s call them a, b, c, d, and e) and we have to break them down into pairs. So how many pairs are possible in a group of five distinct entities?

We could use the combinations formula: ,

where n is the number of items you are selecting from (the pool) and k is the number of items you are selecting (the subgroup).

Here we would get .

So there are 10 different pairs in a group of 5 individuals.

However, in this particular case, it is actually more helpful to write them out (since there are only 5 ghouls and 10 pairs, it is not so onerous): ab, ac, ad, ae, bc, bd, be, cd, ce, de. Now, on the first night (Monday), any one of the ten pairs may be assigned, since no one has worked yet. Let’s say that pair ab is assigned to work the first night. That means no pair containing either a or b may be assigned on Tuesday night. That rules out 7 of the 10 pairs, leaving only cd, ce, and de available for assignment. If, say, cd were assigned on Tuesday, then on Wednesday no pair containing either c or d could be assigned. This leaves only 3 pairs available for Wednesday: ab, ae, and be.