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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The last blog post I wrote showed how modifiers can fool people on quant problems “ here’s the link.

Several of my students who got the baseball problem from that post correct dismissed the issue entirely and scoffed at me for showing them such an easy problem, then inevitably missed a variant of the problem I’m about to show you. Try it for yourself, and watch out for the modifiers!

The town of Malmo, Sweden has only two late-night food options: Pizza and Kebab. All sellers of late-night food have either a street permit or a permanent store permit. 60% of all the late-night food sellers in Malmo are street vendors that serve Kebab; 20% of all the late-night food sellers who have a permanent store serve Pizza. If Malmo’s ratio of total street permits to total permanent store permits is exactly 7 to 3, what percentage of all late-night food sellers in Malmo serve pizza?

 

(A)  10%

(B)  16%

(C)  24%

(D) 30%

(E)  70%

(If you’re not sure how to approach this problem, try brushing up on overlapping sets, covered in the Manhattan GMAT Word Problems strategy guide. Then come back and give it a shot.)

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Most people don’t like weighted averages, and for good reason. The formula is complicated, and these often come in the form of story problems, which are hard to set up. We’re going to talk today about a couple of great little techniques to make these fast and easy well, easier anyway!

First, try this GMATPrep problem. Set your timer for 2 minutes. and GO!

*  A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbit’s diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

 

(A) 100

(B) 140

(C) 150

(D) 160

(E) 200

Wow. I’m glad I don’t have to feed this rabbit. This sounds annoying. : )
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On October 13, 2012, one of the major sports books in Las Vegas said that there was a 108.8% chance of one of the four teams left in the baseball postseason would win the World Series. Of course it didn’t actually say there was a 108.8% chance of this happening, but the odds that they released to bettors did and helped ensure that over the long run, Vegas wins and we, as a whole, lose.

If you haven’t already, check out Part 1 for a review of AND vs OR probability. Now let’s imagine that instead of betting on outcomes, like we did in the previous article, you’ve wised up and decided to open your own sports book, gMATH. You decide to start simple and offer bettors a chance to bet on which number, 1-4, randomly rolls out of a bingo cage. You realize that the probability of each number being selected is 25%, but you need a way to translate this for paying bettors. In a scenario where four different people each put down $1 on each of the four numbers, one person would win $3 ($4 total – $1 they bet). So you place the very first odds at gMATH’s number guessing game at 3 to 1.

In the long run, gMATH’s inaugural betting event may attract a clientele of people who enjoy watching ping pong balls with painted numbers roll around, but it won’t be bringing you the fortunes that you passed up on business school for. You realize that you need a new betting game that will attract more than just the bingo-loving crowd, involves a small amount of luck, and allow you to make a profit no matter which team wins. As there are exactly four teams left in the postseason, you decide that baseball would make a perfect switch.
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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.

I was hanging out with a friend of mine the other day. She is a graduate student, and she asked me a question that she had come across during her research: Read more

In honor of Gabby Douglas’ gold medal win, as well as the U.S. women’s gymnastics team’s all-around gold medal win, here is an Olympics-inspired Data Sufficiency problem.

A particular gymnastics tournament awards a gold, a silver, and a bronze medal in each of four events: Floor, Beam, Bars, and Vault. A platinum Best All-Around medal is awarded to the competitor who gains the most points from winning the other medals: 3 points for gold, 2 points for silver, 1 point for bronze. If McKenzie won the Best All-Around medal, and no one can win more than one medal in any of the four events, did she win at least one gold medal?

1. All of the gold, silver, and bronze medals were won by fewer than six competitors, including McKenzie
2. Another competitor in the tournament has 8 points.

(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.

Choose your answer before proceeding!

First, you may ask, How could someone win the All-Around without winning a single gold medal?

Easy “ just imagine that McKenzie won ALL of the silver medals (8 points), and that no one else won more than one medal (the other medals are won by 8 separate people), so each person who has a gold has just 3 points, and each person who has a bronze has just 1 point.

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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.

Take a look at the following problems.

Data Sufficiency: What was Company X’s percentage profit in 2011?

1) The ratio of costs to profits for Company X was 3 to 1 in 2011.

2) Company X’s costs in 2011 were $360,000.

A recipe for punch calls for 4 parts seltzer to one part juice. If John wants to make 5 gallons of punch, how many 8 ounce cans of juice does he need (1 gallon = 128 ounces)?

A) 32

B) 20

C) 16

D) 10

E) 8

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How can the GMAT disguise a prime number (or any other) problem? I asked this question a couple of years ago at the start of a very important article entitled Disguising “ and Decoding “ Quant Problems. Go read that article right now, if you haven’t already. I’ll wait.

Towards the end of that article, I referenced two Official Guide  problems. I was very excited today to see that one of these problems is part of the free practice problem set that now comes with the new GMATPrep 2.0  software “ so I can actually reproduce it here and we can try it out!

Disclaimer: this is a seriously challenging problem. Set your timer for 2 minutes, but practice your 1 minute timing here. If you don’t have a pretty good idea of what’s going on by the halfway mark, try to figure out how to make a guess. Pick an answer by the 2 minute mark (all right, I’ll let you go to 2 minutes 30 seconds if necessary “ but that’s all!).

Does the integer k have a factor p such that 1 < p < k?

(1) k > 4!

(2) 13! + 2 < k < 13! + 13

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I don’t have a great title for you because I don’t have a really clean category for this question “ and that’s exactly why it caught my attention and why I’m sharing it with you today.
Try out this GMATPrep problem:

Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?

(1) The 3 members sold a total of 6 raffle tickets yesterday.

(2) No 2 of the members sold the same number of raffle tickets yesterday.

This really does not look like a tough question does it? It looks easy! We can’t know for sure exactly how this question was rated, but consider this. I received this as the 15th question in my GMATPrep quant section. Up until that point, I had missed 2 questions, #6 and #14.

By the way, I took the test on a plane without scrap paper and the two I missed were both geometry questions for which I really needed to draw something out. Don’t try that at home! Write everything down. (After #14, I got a napkin from the flight attendant and started using that!)

So, yes, I’d missed the question right before (#14), but I had also gotten 12 of 14 questions right so far. In other words, the above question is at the upper end of the range.

So, the question is harder than it looks. Let’s talk about why. = )

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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