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 many integer values of x satisfy the relationship x⁴ “ 4x³ “ 4x² +16x ≤ 0?

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The other week, we discussed the overall process for Data Sufficiency. This week, we’re going to test out the process using a GMATPrep question “ and take a look at a couple of very common DS traps.

Set your timer for 2 minutes. and GO!

*  A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul all bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50.

(2) Paul bought 4 paperback books and 6 hardcover books for $25.00.

Note that I haven’t listed the answer choices for you. Because DS answers are always the same, we should memorize them. If you don’t have them memorized yet, look back at the How DS Works article linked in the first paragraph.

All right, let’s tackle this problem.

Step 1: Read the Question Stem

The first sentence tells us that each paperback book sells for the same price and each hardcover book also sells for the same price (but possibly a different price than the paperback books).

The question asks how much Maria paid for 1 of each type of book. Is this a value or a yes/no question?

They’re asking for a specific amount; this is a value question. We’ve also got lots of words; we’re going to have to translate.

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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:

A regular octagon (a polygon with 8 sides of identical length and 8 identical interior angles) is constructed. Next, an equilateral triangle (with sides identical in length to those of the octagon) is attached to each side of the octagon, such that each side of the octagon coincides exactly with the side of the triangle. Finally, each triangle is folded over that coincident side onto the octagon, covering part of the latter’s area. Approximately what proportion of the area of the octagon is left uncovered?

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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:

Is xy an integer?

(1) x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square.

(2) y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.

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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:

A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability of generating an odd prime digit is between

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This week, we’re going to talk about what to know for consecutive integer problems and how to recognize what to do on future problems of the same type.

This one is from GMATPrep. Set your timer for 2 minutes. and GO!

*  If n is a positive integer and r is the remainder when n² “ 1 is divided by 8, what is the value of r?

 

(1) n is odd.

(2) n is not divisible by 8.

The first thing you’ll probably notice: I didn’t include the answer choices. The five Data Sufficiency answer choices are always the same, so we should have those memorized. If you don’t have them memorized yet, add this to your to do list.

Just in case, here are the five choices (in casual language, not official language):

(A) statement 1 works but statement 2 does not work

(B) statement 2 works but statement 1 does not work

(C) the statements do NOT work alone, but they DO work together

(D) each statement works by itself

(E) nothing works, not even using them together

Okay, now that we’ve got that out of the way, let’s tackle this problem! This one’s a theory question; they’re asking us about the concept of consecutive integers (as opposed to asking us to do more straightforward calculations with consecutive integers) and they’re not even nice enough to tell us straight out that this is about consecutive integers! We have to figure that out or “ even better “ recognize it.

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What’s more valuable on the GMAT? Saving 30 seconds on a question that took you 2:30 to solve? Or 30 seconds on a question that took you 1:30 to solve? Trick question. Either way, you have the same amount of extra time to use on some other question. So with that in mind, take out a timer, pen, and paper, and let’s try out a fairly straightforward GMATPrep problem.

 

District	Number of Votes	Percent of Votes for Candidate P	Percent of Votes for Candidate Q
1	800	60	40
2	1,000	50	50
3	1,500	50	50
4	1,800	40	60
5	1,200	30	70

 

The table above shows the results of a recent school board election in which the candidate with the higher total number of votes from the five districts was declared the winner. Which district had the greatest number of votes for the winner?

 

(A)  1

(B)  2

(C)  3

(D)  4

(E)  5

Now before we work through the problem. Ask yourself a few questions about what you just did:

1. How confident are you in your answer?
2. How much time did you take to answer?
3. Looking back on your solution, was there shortcut you could have used to eliminate some of the work you did?
4. If so, what specifically about this problem allows you to use your shortcut?

At this point, hopefully you either did the shortcut for this problem or discovered what the shortcut might be. Let’s start with the long method. If I wanted to calculate the number of votes for each candidate, it would look like this:

Twelve calculations later (ten products and two sums), we have all of our numbers calculated and can answer two questions:

1. Who won the election? (Candidate Q)
2. Which district had the most votes for that candidate? (District 4- answer D)

Let’s go back for a second though. Are there any calculations from above that we could have skipped? Let’s start by analyzing the first question from above. Who won the election?

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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:

If x is a prime number, the function G(x) is defined as the xth root of the product of all distinct primes less than or equal to x. If x is one of the first five primes, the maximum value of G(x) occurs when 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:

For all non-negative integers x and n such that 0 ≤ x ≤ n, the function f_n(x) is defined by the equation f_n(x) = x^n“x. The smallest value of n for which the maximum of f_n(x) occurs when x = 4 is

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Did you ever have one of those anal teachers in high school math or science who would take off points if you did not include the correct units? So an answer of 7 would only receive partial credit when the answer was 7 inches.  Although this practice likely seemed frustrating at the time, I hope to provide some method behind this madness “ or specifically how awareness of units can help you on the GMAT.

My appreciation of units first began during college. I was a chemistry major in college, and as part of my major I had to take physics.  The topics in physics never came naturally for me so I was always looking for little tricks that would lead me towards a correct answer.  One trick I found that was surprisingly effective was to just combine the numbers in the way such that the answer was in the appropriate units.  For example if the question asked for an acceleration (the rate at which speed is changing or the second derivative of distance for the calculus-inclined), I knew that acceleration is always in the form of units of distance / units of time^2 (e.g. meters/ seconds^2).  So unless I combined the numbers in a way that resulted in these units as the answer “ for example by dividing a speed in meters per second by a time in seconds “ I knew I had done something wrong.

Since units are not required on the GMAT, I find many students exclude them entirely from their note taking and calculations.  But keeping track of units, while it may cost a little time, can help lead you towards right answers and prevent you from doing illogical algebra.
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