If

xandyare integers such thatx<yandxy= 4, which of the following could be the value of 2x+ 4y?

** To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.**

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

xandyare integers such thatx<yandxy= 4, which of the following could be the value of 2x+ 4y?

** To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.**

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

nis a positive integer greater than 1, then the functionp(n) represents the product of all the prime numbers less than or equal ton. Which of the following is the second smallest prime factor ofp(11) + 12?

** To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.**

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.

- 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.**

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* + 30*y* – 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* + 30*y* – 30 = 600. Subtracting the 600 from both sides, and adding an *x* to each side gives us 30*y* – 30 = *x.* We can now substitute for *x* in the first equation.

If

xis a positive integer and the first nonzero digit in the decimal expansion of is in the hundredths place, what is the value ofx?

**Submit your pick over on our Challenge Problem page.**