When under pressure, do you tend to sit back and assess the situation in a thoughtful way, or do you instead recall everything you know and start jotting down formulae such as W=RT on your scratch paper? If you have a tendency for the latter, this blog post is for you.

I’ve recently had a few tutoring students who all suffered from the same issue: they try a problem in a relaxed state and can easily solve it, sometimes without even putting pen to paper… But when they are in the midst of a practice test (and even more so in a real test) they can see the same problem and spend 4 minutes on it, with a lot of messy algebra, and often times they just give up and move on (the right thing to do under that circumstance!).

The Quant section of the GMAT may feel like a math test, but I assure you it is not. It is a cleverly designed assessment of your thinking faculties, and if you turn on ‘autopilot’ you are no longer thinking. In order to succeed on this test, you have to think your way through each problem.

When I take the GMAT, I imagine that I’m hanging out with my buddies at the bar – we’re telling each other jokes and sharing brain teasers. Here’s how it works:  you’re all just out having a good time, there’s no pressure, maybe you’ve had a couple of drinks so you only try to solve those brain teasers that you think you can solve in 2-3 minutes or less. If the brain teaser seems too hard, you just give up (and no-one will think less of you!)

I suspect that your approach to the following problem would be completely different if your mindset is a ‘bar’ mindset vs. an ‘autopilot’ mindset:

I’m driving at a constant speed and it took me 4 hours to finish the first 1/3 of my trip. How long will it take me to complete the rest of the trip if I double my speed?

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We were taught in school to think of whole numbers in the context of two groups: Odds vs. Evens. I remember thinking it was like the black vs. white pieces on a chess board (I was kind of a nerd). As I’m sure you know, an Even number is simply a number divisible by 2, and an Odd number is any number that’s not even. But ask yourself this: what is the remainder when you divide an odd number by 2? Take a minute to think about this. Try out a few different odd numbers and see if you can identify a pattern.

The remainder will always be 1 when you divide an odd number by 2. Always. And when you divide an even number by 2? Well, by definition the even number is divisible by 2, so the remainder is therefore zero.

The GMAT loves taking this concept and testing how deep your understanding goes. Therefore, we must free ourselves of the simplistic odd vs. even framework that we were fed in school, and explore this concept to a much deeper level. That is exactly what I intend to do in this blog post.

I always joke with my students that if I were the number 3 on the number line, I would really hate my next door neighbor to the left (number 2). He thinks he’s so special because there’s a name for any multiple of him (“even”); and if that’s not enough to give him a big head, they also invented a name for any number that isn’t a multiple of him (“odd”). What do you call multiples of me? “multiple of 3”. What do you call numbers that are not multiples of me? “not a multiple of 3”. LAME

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Are you ready for a challenge? Try to solve the following question in under two minutes:

How many different positive divisors does the number 147,000 have?

If you feel like two minutes are not nearly enough to solve the problem, you’re not alone. Even the most seasoned GMAT veterans might find the problem challenging, as it requires a deep level of understanding of two mathematical concepts: Divisibility and Combinatorics (just a fancy word for ˜counting’).

If I replaced the number 147,000 with the number 24, many more people would be able to come up with an answer:

You could just pair up the divisors (factors) and count them. Start with the extremes (1×24) and work your way in:

1×24

2×12

3×8

4×6

A quick count will show the number 24 has exactly 8 different positive divisors.

The number 147,000 will have many more positive divisors “ too many to count This is a strong indication that we will need to use combinatorics.

Divisibility: Any positive integer in the universe can be expressed as the product of prime numbers.
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Try to solve the following question, and time yourself:

If the volume of a big cube is 64 times that of a small cube, how many times bigger is the surface area of the big cube than that of the small cube?

If you cannot answer the above (classic GMAT) question in under 20 seconds, continue reading and you will learn a concept that will be super useful in your quest to crush the GMAT!

I was watching Austin Powers the other day and it suddenly hit me: Dr. Evil and Mini-Me are similar shapes! You know, like similar triangles, where the proportion between any two matching sides is always maintained “ if Mini-Me’s fingers are exactly half the length of Dr. Evil’s fingers, then Mini-Me’s eyes, ears, nose, and feet must also be exactly half their counterparts in Dr. Evil’s body. It got me thinking “ what other kinds of similar shapes could be out there? I will investigate that thought further in the second half of this post, but first let’s see why that might be useful

We know triangles are similar whenever they have the same three angles. If the base of the bigger triangle is exactly twice that of the smaller triangle, then each side in the bigger triangle will also be twice as big as its matching side in the smaller triangle.
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Most students who struggle with Reading Comprehension share a common issue: they focus equally on all words in the passage. Some words, however, are not as important as others, and in order to improve our comprehension we must first learn to identify which words we should focus our energy on. You may have noticed that the title of this blog post is difficult to follow; words such as unlike and not are important structural words, since they describe a 180 degree change in meaning. If we speed through the title we are likely to miss something important, and our comprehension level will drop! Instead, let’s come to a complete stop and hold off on the rest of the post until we have milked those structural words for all they’re worth.

The title first makes a comparison (actually an anti-comparison) between words and people, and then separately says that words are not all born equal (for a moment we can ignore the modifier trapped between the commas).

If words are not all born equal, and words are unlike people, one could infer that all people are born equal. Did you get that from the title when you first read it? If you didn’t, you read it too quickly

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If you’ve read my previous post you know I got married very recently. When I asked my new wife the other day to name her favorite celebrity, she said Ryan Gosling; unfortunately I look nothing like him “ so I’m not quite sure where that leaves me. As a form of revenge I’ve decided to use Mr. Gosling to demonstrate some key insights in the commonly misunderstood topic of Weighted Average. Ryan will never forgive me!

For the purpose of this blog post let’s assume that Ryan Gosling made $10M per movie in 80% of his movies and $20M per movie in 20% of his movies. His average paycheck would have been $15M if his salary were distributed evenly between $10M and $20M “ but an 80-20 distribution means we’ll have to put a little more thought into the situation. If we want to know how much Mr. Gosling made on average per movie, we have no choice but to calculate the weighted average.

Some math lovers might use an algebraic formula to calculate the weighted average, but I believe using a visual approach for this calculation will drive a deeper level of understanding for us regular folks.

Use your intuition and try a visual approach

If I asked you for a range of the weighted average of Ryan Gosling’s paychecks, your intuition would probably suggest between $10M and $20M. You might even propose that the weighted average be closer to $10M than to $20M (since $10M has a heavier weight “ 80% vs. 20%). You would be absolutely correct!

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Editor’s Note: This is the first post by Manhattan GMAT instructor Avi Gutman. Toronto-based, England-born (to Scottish and Moldovan parents), and Israel-raised, Avi likes to consider himself an international man of mystery. The publication of this post was delayed a week due to Avi’s wedding! Welcome him to our blog and send him your congratulation in the comment section below!

Raise your hand if you cringe whenever you think of word problems from 8th grade. Raise your hand again if you feel queasy when you see a question involving Train A and Train B.

If your hand is getting tired this blog post is for you. Most of us already know that GMAT problems involving moving objects (people, cars, trains, etc.) are just one particular form of a WRT (Work Rate Time) problem, where the work is simply the distance traveled. When dealing with just one moving object we can apply the DRT formula as usual (Distance=Rate*Time), but the test writers know that by throwing two moving objects at us (figuratively!) they raise the level of the problem by some 200 points.

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