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:

Z is the set of the first n positive odd numbers, where n is a positive integer. Given that n> k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of Z, and y is the minimum value of the sum of k distinct members of Z, what isx + y?

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Recently, I gave you a GMATPrep question and started out by asking What is this thing, anyway? I’ve got another one (along similar lines) for you this week (also a GMATPrep problem).

By the way, I love this problem. Yes, I know I’m a complete dork. But it does such an amazing job of disguising what’s going on, and it looks deceptively simple, but then it’s hard to figure out an efficient way to tackle it. There’s so much to learn on this one “ that’s why I love it.

Try it out (2 minutes!):

Are x and y both positive?

(1) 2x “ 2y = 1

(2) x/y > 1

It can’t be that hard, right? It’s just asking whether they’re positive, and the equation and inequality look pretty simple, and well, let’s see how we do.

This is a theory question, first of all. How do we know that? Because they’re asking whether something is true, that thing is a characteristic (in this case, positive), and the information they give us is clearly not enough to determine a single value for x and y. Therefore, those statements are actually disguising other characteristics that can help us to tell whether these variables are always positive. Read more

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 any numbers a and b, min(a, b) and max(a, b) represent the minimum and the maximum of a and b, respectively. If c > a, is a < b < c?

(1) min(max(a, b), c) = max(min(b, c), a)

(2) max(max(a, b), c) “ min(min(b, c), a) > c “ a

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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 positive integers n, the integer part of the nth term of sequence A equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, A₁ = 1.2345678…, while A₂ = 2.4681012… The sum of the first seven terms of sequence A is between

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Let me start off by saying that hard work and mastering each question topic is the best way to conquer the GMAT. There is no Up-Up-Down-Down-Left-Right-Left-Right B, A, Start cheat code that can replace months of intense studying. That said, getting a 700+ score on the GMAT sometimes means having a few tricks up your sleeves. Here’s a few strategies that I’ve found to be helpful with gaining a few extra points at the very top of the GMAT curve:

1) Know your PEMDAS and your SADMEP

 In other words, you have to know your parenthesis, exponents/roots, multiplication, division, addition, and subtraction, backwards and forwards. For as many students as I have worked with, I have yet to come across a student who can barely work through a multiplication table, yet still manages to consistently finish the quant portion of the GMAT. Even though you only need to answer 37 quantitative questions, this will entail hundreds of math calculations- calculations that far too many of us have left to the machines (I for one welcome our new calculator overlords). If the average straightforward calculation takes five seconds and a student sees two hundred of these calculations over an average test, that’s sixteen minutes and forty seconds of just doing simple arithmetic. And if it takes you twice as long to do each of those calculations, that’s going to take, umm, well, it’s…. it’s going to take a lot longer.

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Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

In a world where we are often carrying at least one device, if not multiple devices, that can complete calculations, there is little need to do calculations manually. For this reason, the lack of a calculator on the GMAT Quantitative section is a significant point of concern—or perhaps even fear—to many test takers, even some with strong quantitative skills. That brings me to some good and some bad news for prospective GMAT takers. Read more

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:

1. x[1]y = x^y
2. If n is odd, x[n+1]y = (x[n]y)^x
3. If n is even, x[n+1]y = (x[n]y)^y

If y = ½ and x[4]y = 2, then x =

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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?

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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?

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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

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