### Monthly GMAT Challenge Problem Showdown: January 13, 2013

We invite you to test your GMAT knowledge for a chance to win! The second week of every month, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that month’s drawing for free Manhattan GMAT prep materials. Tell your friends to get out their scrap paper and start solving!

Here is this month’s problem:

If

p,q, andrare different positive integers such thatp+q+r= 6, what is the value ofx?(1) The average of

xand^{p}xis^{q}x.^{r}(2) The average of

xand^{p}xis not^{r}x.^{q}

### GMAT Challenge Problem Showdown: December 23, 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 pharmacy must purchase a set of

nmetal weights, each weighing an integer number of grams, such that all integer weights from 1 to 300 grams (inclusive) can be made with a combination of one or more of the weights. What is the minimum number of metal weights that the pharmacy must purchase?

### GMAT Challenge Problem Showdown: December 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:

A set of

nidentical triangles with anglex° and two sides of length 1 is assembled to make a parallelogram (ifnis even) or a trapezoid (ifnis odd), as shown. Is the perimeter of the parallelogram or trapezoid less than 10?

### GMAT Challenge Problem Showdown: December 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:

Can you find the most efficient way to solve this problem?

Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of six chairs. How many seating arrangements are possible if Gita cannot sit next to Inge and Jeong must sit next to Leila?

### GMAT Challenge Problem Showdown: December 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:

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)

### 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