Challenge Problem Showdown – May 7th, 2012
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 expression x[n]y is defined for positive values of x and y and for positive integer values of n as follows:
- x[1]y = xy
- If n is odd, x[n+1]y = (x[n]y)x
- If n is even, x[n+1]y = (x[n]y)y
If y = ½ and x[4]y = 2, then x =
Challenge Problem Showdown – April 30th, 2012
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:
From 2008 to 2009, the number of Easter eggs in a certain egg hunt rose 20%, then fell 17% from 2009 to 2010. From 2008 to 2009, the ratio of Easter eggs to Easter bunnies in the same hunt fell 20%, then rose 22% from 2009 to 2010. By what approximate percent did the number of bunnies change over the full period from 2008 to 2010?
Challenge Problem Showdown – April 23rd, 2012
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:
Ror positive integer m, the m-th heptagonal number is given by the formula 5m2 “ 3m)/2. For positive integer n, the n-th triangular number is the sum of the first n positive integers. Which of the following is true for k, the smallest triangular number that is also heptagonal?
Challenge Problem Showdown – April 16nd, 2012
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 value of x that satisfies the equation (1 + 2x)5 = (1 + 3x)4 is between
Challenge Problem Showdown – April 9nd, 2012
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 expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#42?
Challenge Problem Showdown – March 19th, 2012
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:
(1.0002)(0.9999) “ (1.0001)(0.9998) =
Challenge Problem Showdown – March 12th, 2012
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:
What is the absolute difference between the cubes of two different non-negative integers?
(1) One of the integers is 2 greater than the other integer.
(2) The square of the sum of the integers is 49 greater than the product of the integers.
Challenge Problem Showdown – March 5th, 2012
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 integers a, b, c, and d can each be equal to 0, 1, 2, or 3, independently.
What is the value of (a + 1)(b + 1)(c + 1)(d + 1)?(1) a + 4b + 16c + 64d = 165
(2) 64a + 16b + 4c + d = 90
Challenge Problem Showdown – February 26th, 2012
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 much greater is the square of the sum of three different positive integers than the sum of their squares?
(1) The sum of the products of all possible pairs of two different integers out of the original set of three is 61.
(2) The largest of the three integers, 7, is equal to the sum of the two smaller integers.
Challenge Problem Showdown – February 21st, 2012
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!
Two integers between 1 and 100, inclusive, each randomly and independently chosen, are either added or multiplied, with an equal chance of either operation. What is the probability that the result is even?