Articles tagged "quant"

GMAT Challenge Problem Showdown: August 12, 2013

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challenge problem
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 how many unique pairs of nonnegative integers {a, b} is the equation a2 – b2 = 225 true?

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GMAT Challenge Problem Showdown: August 5, 2013

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challenge problem
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 coin purse contains 13 coins, each worth 1, 5, 10, or 25 cents; the total value of the coins is 150 cents. How many 10-cent coins are in the purse?

(1) The 13 coins can be divided among five separate envelopes so that each envelope contains the same total monetary value.

(2) The 13 coins can be divided among six separate envelopes so that each envelope contains the same total monetary value.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

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GMAT Challenge Problem Showdown: July 29, 2013

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challenge problem
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 total of m different points are selected on a particular line, and a total of n different points are selected on another line parallel to the first, where each of m and n is greater than 1. In how many different ways can a triangle be made with its vertices at three of the selected points?

A. m2n + mn2

B. mn(m + n – 2)

C. 

D. 

E. 

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Another Way To Solve Median & Mean Questions

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gmat median & meanThis is the second of a series of posts that offer alternate ways to solve certain GMAT problems (check out the first here: DS Value Problems). Just like last time, if you like the method, steal it! And if you don’t, I promise not to lose any sleep. There’s a lot of ways to solve most questions on the GMAT and the best way will always be the way that works best for you. So without further ado, let’s check out a GMATPrep question and see how fast you can solve:

Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $165,000.

II. At least one of the homes was sold for more than $130,000 and less than $150,000.

III. At least one of the homes was sold for less than $130,000.

 

(A) I only

(B) II only

(C) III only

(D) I and II

(E) I and III

First things first, if you answered this question using algebra, you’re in great company. Another one of our instructors, Stacey Koprince, has a great write up on the algebra in this question, and it’s definitely worth a read-through right here. But a lot of questions on the GMAT, including this one, can be solved by thinking of extremely simple scenarios, rather than the algebra that determines all of them.

The first thing I noticed on this question is that this is one of those awful questions where there’s a whole lot of wiggle room with the information that they give you. What was the cheapest house? What was the cost of the third most expensive house? Were any of the houses all the same price? If the second cheapest house is half as expensive as the most expensive, how does that affect the cost of the other houses? It’s easy to get lost when you start to think about how little you know in this scenario.

But before I jump around and start picking values out of thin air, the most important part of this problem are the (few) things that MUST be true. In this case, there are two: the 15 house prices have a mean of $150,000 and a median of $130,000. And on my paper, I would write out a few slots to represent the house prices like this: (note- I wouldn’t write out all 15 slots. Just the first few, the last few, and, since this is a median problem, one in the middle.)

 

____

____

____

____

____

1

2

7

14

15

 

Again, there are two things that they tell me here, but I want to start with the most restrictive element in this problem. There are lots of different ways to get a mean of $150,000, but in order to get a median of $130,000, I would need at least one house to cost EXACTLY $130,000. So I add that to my chart (ignoring the $ sign and extra zeroes):

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GMAT Challenge Problem Showdown: June 24, 2013

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challenge problem
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 point Q is located within the interior of a square ABCD so that it is 1 unit from vertex A, 2 units from vertex B, and 3 units from vertex D. The measure of angle AQB is

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GMAT Challenge Problem Showdown: June 17, 2013

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challenge problem
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:

Triangle ABC is cut by a line DE parallel to side AC, as shown in the diagram. If side AC has length 1, and the area and perimeter of triangle ABC are both twice the corresponding values for trapezoid ADEC, what is the perimeter of triangle DBE?

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Want a 750+? Think Your Way Through This Challenge Problem!

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gmat 750+A few months ago, I wrote a couple of articles targeted toward those students looking for a super-high score (one for quant, one for verbal). I challenged students to answer those questions in much less time than we typically average on test questions.

Well, I’m back with another one in the series. This problem is a bit different though: it’s from our Challenge Problem archive, a question bank consisting of what we call 800+ level problems. (Some might qualify as 750+ but most are harder than anything you’ll ever see on the real test.)

Do you need to be able to answer a question like this in order to score 750+? Absolutely not. (In fact, after my colleague Ron Purewal submitted this question, I tested it out on several of my fellow instructors, all of whom have scored 760+ on the test. Not everyone answered correctly.) Mostly, I’m offering this to stretch your brains, drive you a little crazy, and make one important point (see my second takeaway at the end).

If, however, quant is your strength and you’re hoping to score 51 in that section”you can certainly score 51 without getting this one right, but if you do get this one right in 2 minutes, then you know you’re ready for the quant section.

One more tidbit before we dive in. I chose this question because it is SO very hard. As of right now (as I’m typing this), 254 people have tried this problem and 44 have answered it correctly.

Do a little math here. What percentage of people answered the question correctly?

17%. Random guess position is 20%. Wow.

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GMAT Challenge Problem Showdown: May 20, 2013

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challenge problem
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 octagon in the diagram above is regular: all of its sides are of equal length, and all of its angles are of equal measure. If the octagon’s perimeter is 8 inches, and every other vertex of the octagon is connected to create a square as shown above, what is the area of the square?

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Challenge Problem Showdown- April 29, 2013

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challenge problem
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:

In a certain type of tiling called Penrose P3 tiling, two types of rhombi fill a space without gaps or overlaps: wide rhombi and narrow rhombi. If five of the wide rhombi can meet symmetrically at a single point, while ten of the narrow rhombi can, what is the ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus?

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What is this Quant Question Hiding?

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A certain class of questions tends to have more going on than might be apparent on the surface. (I’m being intentionally vague as to the certain class “ I’ll tell you what it is after you’ve tried the problem!)

Give yourself approximately 2 minutes to try the below GMATPrep problem. When you’re done, take a look at it again and ask yourself, What was this testing? What was it hiding?

*  If n is a positive integer and r is the remainder when (n “ 1)(n + 1) is divided by 24, what is the value of r?

(1)  n is not divisible by 2.

(2)  n is not divisible by 3.

Got something for me? Sure?

what's this gmat quant questions hidingLa la la. I’m just adding words here so that you don’t inadvertently glance down and see the answer while you’re still figuring things out up above. : ) Okay, what are the clues? Integer and remainder tell us that this is likely a number properties problem “ this is the class I was referring to earlier. I can tell this is number properties from a couple of key words, but it turns out there’s even more going on. The words divided by bring up the idea of divisibility. Finally, the problem begins by talking about the variable n, but also later mentions n “ 1 and n + 1. Put those three terms together and what have we got? Consecutive integers!

So we’re going to need to think about consecutive integer properties for 3 numbers in a row, and yet the divisibility info in the question stem talks only about the first and third numbers, while the info in the statements refers to the middle number. Okay.

Are any rules popping up in your mind right now? What have you learned about consecutive integers in the past, in particular for a set of 3 consecutive integers?

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