### GMAT Challenge Problem Showdown: October 21, 2013

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 sheet of paper

ABDEis a 12-by-18-inch rectangle, as shown in Figure 1. The sheet is then folded along the segmentCFso that pointsAandDcoincide after the paper is folded, as shown in Figure 2 (The shaded area represents a portion of the back side of the paper, not visible in Figure 1). What is the area, in square inches, of the shaded triangle shown?

### GMAT Challenge Problem Showdown: October 14, 2013

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

a,c,d,x, andyare positive integers such thatay<xand is the lowest-terms representation of the fraction , thencis how much greater thand? (If is an integer, letd= 1.)(1) is an odd integer.

(2)

a= 4

### GMAT Challenge Problem Showdown: October 7, 2013

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 positive number

aisqpercent greater than the positive numberb, which isppercent less thanaitself. Ifais increased byppercent, and the result is then decreased byqpercent to produce a positive numberc, which of the following could be true?I.

c>a

II.c=a

III.c<a

### GMAT Challenge Problem Showdown: September 30, 2013

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 different pairs of positive integers (

a,b) can the fraction be written as the sum ?

### GMAT Challenge Problem Showdown: September 16, 2013

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

aandbare different nonzero integers, what is the value ofb?(1)

a=^{b}ab(2)

a–^{b}a^{b}^{ – 1}= 2

### GMAT Challenge Problem Showdown: September 9, 2013

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 semicircular piece of paper has center

O, as shown above. Its diameterA’Ais coated with adhesive. If the adhesive is used to fuse radiiOA’andOAalong their entire lengths (so that pointsAandA’ coincide, pointsPandP’ coincide, and so on), a cone is formed as shown above. If pointBdivides the original semicircle into two identical arcs, what is the measure of angleAOBin the folded cone?

### GMAT Challenge Problem Showdown: September 2, 2013

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 8am on Thursday, two workers, A and B, each start working independently to build identical decorative lamps. Worker A completes her lamp at 5pm on Friday, while Worker B completes her lamp sometime during the morning on Friday. If both workers adhere to working hours of 8am to 12pm and 1pm to 5pm each day, at which of the following times might the two workers have completed a single lamp had they worked together at their respective constant rates?

### GMAT Challenge Problem Showdown: August 26, 2013

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?

### GMAT Challenge Problem Showdown: August 19, 2013

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,

ABCis a right triangle withACas its hypotenuse, andPQRSis a square. What is the area of the square?(1)

ACis 70 units long.(2) The product of the length of

ASand the length ofRCis 396.

### GMAT Challenge Problem Showdown: August 12, 2013

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

a^{2}–b^{2}= 225 true?