The Math Beast Challenge Problem of the Week – November 25, 2013
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If n is a positive integer greater than 1, then the function p(n) represents the product of all the prime numbers less than or equal to n. Which of the following is the second smallest prime factor of p(11) + 12?
To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.
The Math Beast Challenge Problem of the Week – November 18, 2013
Orren drove from his home to work in the morning at x miles per hour, and returned home in the evening at y miles per hour. His average speed for the round trip was 60 miles per hour.
Quantity A Quantity B
x 30
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.
The Math Beast Challenge Problem of the Week – November 11, 2013
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.
The Math Beast Challenge Problem of the Week – November 4, 2013
Positive integer n leaves a remainder of 2 after division by 6 and a remainder of 4 after division by 5. What is the remainder when n is divided by 30?
To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.
Manhattan GRE’s Halloween Challenge Problem
We hope everyone had a happy Halloween! Yesterday we asked our friends on our Manhattan GRE Facebook page to attempt this Trick-or-Treat Halloween Challenge Problem. As promised, today we are sharing the answer and explanation to the problem:
Let’s use x for the number of bags produced by the original recipe, and y for the weight of each of the bags. Given those variables, our first equation is simply xy = 600. We also need to create an equation that represents the new recipe. Since the number of bags produced has increased by 30, and the weight of each bag has decreased by 1, the new equation is (x + 30)(y – 1) = 600. Remember, the total weight is still 600 ounces. Foiling this equation yields xy – x + 30y – 30 = 600.
We now have two equations with two variables. There are several different paths we can go down here, but all involve substitution of one of the variables, and all will yield a quadratic. The simplest path is to recognize that since xy = 600, we can substitute for xy in the second equation to get 600 – x + 30y – 30 = 600. Subtracting the 600 from both sides, and adding an x to each side gives us 30y – 30 = x. We can now substitute for x in the first equation.
The Math Beast Challenge Problem of the Week – October 28, 2013
Each week, we post a new GRE Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.If x is a positive integer and the first nonzero digit in the decimal expansion of
is in the hundredths place, what is the value of x?
is in the hundredths place, what is the value of x?
Submit your pick over on our Challenge Problem page.
The Math Beast Challenge Problem of the Week – October 21, 2013
Each week, we post a new GRE Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.The outer figure above is a rectangle with four rounded corners of radius equal to 2. The inner figure is a circle.
Submit your pick over on our Challenge Problem page.
The Math Beast Challenge Problem of the Week – October 14, 2013
Each week, we post a new GRE Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
Xander, Yolanda, and Zelda each have at least one hat. Zelda has more hats than Yolanda, who has more than Xander. Together, the total number of hats the three people have is 12. If Zelda has no more than 5 hats more than Xander, which of the following could be the number of hats that Yolanda has?
See the answer choices and submit your pick over on our Challenge Problem page.
The Math Beast Challenge Problem of the Week – October 7, 2013
Each week, we post a new GRE Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
See the answer choices and submit your pick over on our Challenge Problem page.
The Math Beast Challenge Problem of the Week – September 30, 2013
Each week, we post a new GRE Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.
A retailer previously bought an item from a wholesaler for $20 and sold it to consumers for a retail price of $35. After a wholesale cost reduction, the retailer reduces the retail price by 10%, yet the retailer’s profit on the item still increases by 20%. By what percent did the wholesale cost decrease?
See the answer choices and submit your pick over on our Challenge Problem page.