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 function F(n) is defined as the product of all the consecutive positive integers between 1 and n², inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is

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Here are the free GMAT events we’re holding this week. All times listed are local unless otherwise specified.

10/15/12 – Toronto, IL – Free Trial Class – 6:30-9:30 PM

10/15/12 – Chicaco, IL – Free Trial Class – 6:30-9:30 PM

10/15/12 – Glendale, CA – Free Trial Class – 6:30-9:30 PM

10/16/12 – Washington, D.C. – Free Trial Class – 6:30-9:30 PM

10/16/12 – San Diego, CA – Free Trial Class – 6:30-9:30 PM

10/16/12 – San Francisco, CA – Free Trial Class – 6:30-9:30 PM

10/17/12 – Online (intended for Russian students) – Reading Comprehension for Russian Speakers Workshop – 8:00-9:30 PM MSK

10/17/12 – Ann Arbor, MI – Free Trial Class – 6:30-9:30 PM

10/17/12 – Houston, TX – Free Trial Class – 6:30-9:30 PM

10/17/12 – Santa Monica, CA – Free Trial Class – 6:30-9:30 PM

10/17/12 – Seattle, WA – Free Trial Class – 6:30-9:30 PM

10/17/12 – Online – Essay Writing Workshop (presented by mbaMission) – 9:00-10:30 PM

10/18/12 – Online – Free Trial Class – 8:00-11:00 PM EDT

10/21/12 – London, UK – Free Trial Class – 2:00-5:00 PM

10/21/12 – Washington, D.C. – Free Trial Class – 5:30-8:30 PM

10/21/12 – West Hollywood, CA – Free Trial Class – 2:00-5:00 PM

10/21/12 – San Francisco, CA – Free Trial Class – 10:00 AM – 1:00 PM

10/21/12 – Online – Free Trial Class – 2:00-5:00 PM EDT

Looking for more free events? Check out our Free Events Listings Page.

Have you ever gotten a GMAT question wrong because you thought you were supposed to take a square root and get two different numbers but the answer key said only the positive root counted? Alternatively, have you ever gotten one wrong because you took the square root and wrote down just the positive root but the answer key said that, this time, both the positive and the negative root counted? What’s going on here?

There are a couple of rules we need to keep straight in terms of how standardized tests (including the GMAT) deal with square roots. The Official Guide does detail these rules, but enough students have questioned us about the OG explanation that we decided to write an article in hopes of clearing everything up. : )

I want to mention one thing before we dive in: the vast majority of the time, both roots do count, and it’s rare to miss an official question as long as you do take both roots. You could just decide that you’re not going to worry about it and you’re going to solve normally (always taking both square roots). Many students do still stress about this topic, though, so if you’re in that group, read on!

Doesn’t the OG say that we’re only supposed to take the positive root?

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Note: This is the first of a two-part series on Probability. The baseball odds used in this article were true on the morning of October 11 and are definitely no longer true. Using this gambling advice will likely cost you money in the long run, as Joe will explain in Part 2.

In terms of excitement, the World Series of Coin Flipping would rate right next to solving Data Sufficiency problems in the general public’s mind. But any Vegas oddsmaker worth his weight in comped beverages would be able to calculate the odds for every coin flipping contest in the time it would take the coin to land. In an 8-team bracket-style tournament, every squad would have 1 in 8 odds to win it all because only 1 team out of the 8 could outguess their way to the championship. But what if each matchup of two teams was a 3 game series? It wouldn’t affect the odds at the beginning of each series (still a 50% probability for each team to win), but once the first outcome was decided, those Vegas oddsmakers would require some knowledge of And Probability to keep the odds fair.

Imagine we have two teams competing in the first round of our Coin Flipping Playoffs- let’s call them Baltimore & New York. In our three game series, New York happened to have some late flipping heroics to go up 1-0. What are the odds that Baltimore comes back in this series and what are the odds that Baltimore comes back and then wins the whole tournament? The key to this type of question is understanding that many things have to go right in order for Baltimore to win it all- first they need to win Game 2, then win the winner-takes-all Game 3, then win their semi-final series, and then still have enough thumb strength to flip the World Series in their favor. Four unique events need to happen, and every single one of those events must happen for Baltimore to emerge victorious. Since the odds of each game and each series going Baltimore’s way would be 1/2, we can solve this by finding the odds that Baltimore wins Game 2 (1/2) AND Game 3 (1/2) AND the next series (1/2) AND the championship (1/2). In probability, whenever we want X AND Y to occur, we need to multiply the respective odds together. The odds of Baltimore winning Game 2 and 3 would be 1/2 x 1/2 = 1/4. The odds of winning all four events would be (1/2)⁴ = 1/16.
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Here are the free GMAT events we’re holding this week.

10/8/12 – Boston, MA – Free Trial Class – 6:30-9:30 PM

10/8/12 – Santa Clara, CA – Free Trial Class – 6:30-9:30 PM

10/9/12 – Online – Free Trial Class – 8:00-11:00 PM

10/10/12 – Chicago, IL – Free Trial Class –  6:30-9:30 PM

10/11/12 – Online – Thursdays with Ron GMAT Study Hall – 7:00-8:30 PM

10/13/12 – Online – Free Trial Class – 2:00 – 5:00 PM

10/14/12 – Boston, MA – Free Trial Class – 6:30-9:30 PM

10/14/12 – Santa Monica, CA – Free Trial Class – 5:30-8:30 PM

10/14/12 – Online – Free Trial Class – 7:00 – 10:00 AM

Looking for more free events? Check out our Free Events Listings Page.

How do you feel when you see a sentence correction with a very substantial underlined section? Overwhelmed, anxious, perhaps even a little bit angry.  Maybe at this point you move to freak out mode thinking I am never going to complete this problem in 1 minute and 15 seconds (recommended average time for sentence correction problems).  I have found that freaking out is never the optimal approach to any GMAT questions, so let’s identify some alternate approaches we can use to our advantage when facing a sentence correction problem with a lot underlined.

1) Lots underlined usually means lots of mistakes.  When a large portion is underlined, there are almost always several mistakes in the sentence, and thus several different ways to get to the answer.  Don’t feel like you have to comprehend everything that is going on in the sentence right away, but rather start with the grammatical principle with which you are most comfortable.  I actually dislike problems with only a few words underlined because these problems often involve only a single issue “ and if I don’t know that particular rule I am in trouble.

2) Use your initial read of the sentence as a jumping off point. Often you may spot an error in the initial sentence.  Instead of trying to completely scan all the answer choices, immediately go to this particular area in each answer choice to see if the problem still exists and eliminate accordingly.
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Here’s a fairly straightforward GMATPrep question that I’ve seen many-a-student answer incorrectly. See if you can answer the question without writing anything down:

Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical?

 

A)  25%

B)  22.2%

C) 20%

D) 12.5%

E)  11.1%

Classic GMAT question. Straightforward. Easy to understand. Simple to equate” 1/3 of 3,600 is 1,200 and 1/3 of that is 400. So we’d only have 800 remaining clerical staff and 800/3600 = 2/9, answer B. And like so(oooooooo) many other GMAT questions, we’d have answered incorrectly.

If have some paper in front of you, try to solve the question again by writing down each step along the way. Maybe even include what each of those numbers that you write down mean in the context of the question. Don’t cheat- see if you answer the question differently when you’re forced to write down more than just a simple computation or two.

…

Here’s what I wrote down first on my scrap paper:
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In an earlier post, we tackled a medium-level GMATPrep weighted average question; click here to read that article before reading this one. This week, we’re trying a harder GMATPrep  weighted average question in order to test whether you learned the concept as well as you thought you did. : )

As we discussed earlier, every weighted average problem I’ve seen (so far!) on GMATPrep is a Data Sufficiency question. This doesn’t mean that they’ll never give us a Problem Solving weighted average problem, but it does seem to be the case that the test-writers are more concerned with whether we understand how weighted averages work than with whether we can actually do the calculations. Last week, we focused on understanding how weighted averages work via writing some equations. We’ll try to apply that understanding to our harder problem this week, along with a more efficient solution method.

Let’s start with a sample problem. Set your timer for 2 minutes. and GO!

* A contractor combined x tons of gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?

(1) y = 10

(2) z = 16

There are two kinds of gravel: 10% gravel and 2% gravel. These are our two sub-groups. When the two are combined (in some unknown “ for now! “ amounts), we get a 3^rd kind:5% gravel. The number of tons of 10% gravel (x) and the number of tons of 2% gravel (y) will add up to the number of tons of 5% gravel (z), or x + y = z. We need to find the number of tons of 10% gravel used in the mixture.

The problem this week throws in a new wrinkle: we’re not just trying to calculate a ratio this time. We have to have enough info to calculate the actual amount of 10% gravel used. Last week, we never had to worry about the actual number of employees. We’ll have to keep that in mind to see how things might change.

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This week, we’re going to tackle a GMATPrep question from the quant side of things. We’ll tackle a medium-level question this week in order to learn how to master weighted average questions in general, and in the next article, we’ll try a very hard one “ just to see whether you learned the concept as well as you thought you did. : )

Before we begin, I want to mention that every weighted average problem I’ve seen on GMATPrep is a Data Sufficiency question. This doesn’t mean that they’ll never give us a Problem Solving weighted average problem, but it does seem to be the case that the test-writers are more concerned with whether we understand how weighted averages work than with whether we can actually do the calculations. So we’re going to work on that conceptual understanding today and then we’ll discuss a neat calculation shortcut next week (built on the same principles!), just in case we do need to solve.

Let’s start with a sample problem. Set your timer for 2 minutes. and GO!
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