Simple Quantitative Strategies for the GMAT

Before you review all that algebra and statistics you’ve forgotten over the years, and before you practice with an endless sequence of practice problems, you should learn a few simple tips that well help you immensely on test day. Learn these early, and reinforce them during practice.

These strategies may appear simple, but they can mean big points in a pressured testing environment. So, when you take a GMAT Practice Test, think about these techniques. They will keep you from making careless mistakes on easy-to-mediate problems, which can end up making a huge difference on a computer adaptive test.

 

More GMAT Math Tricks

Here are a few more quick GMAT math tricks that could save you anywhere from a few seconds to a few minutes on Exam Day. 

Number Properties Tips

• The product of two consecutive integers is always divisible by two, the product of three consecutive integers is always divisible by three, and so on. 
• To check whether a complicated expression is even or odd, plug in 0 and 1. For instance, try the expression 2x3 + x2 + x. If you plug in 0, you get 0, which is even. If you plug in 1, you get 4, which is also even. So, this expression is always even. 
• If you want to find all of the factors of a number by guessing and testing, you can stop when you reach the square root of that number. For instance, if you’re finding all of the factors of 228, you can stop checking numbers when you hit 15, since that’s approximately the square root of 228. 

Geometry Tips

• If you double the side length of a shape (such as a square or triangle), its area quadruples. If you halve the side length, its area is quartered. 
• Learn the three ways to spot similar triangles, so you’ll instantly recognize that two triangles are similar without having to prove it from scratch. 
• If a problem tells you a shape is a rectangle, don’t forget that the shape could be a square! In fact, a square is often a good case to test on Geometry Data Sufficiency problems. 
• If a GMAT math problem asks you whether a point is on a line, plug the coordinates of the point into the equation for the line. If you get a valid result, then the point is on the line. For example, the point (2, 6) is on the line y = 2x + 2.

Word Problems Tips

• The average of a set of numbers always has to be somewhere in the middle of that set. It can’t be larger than the largest number in the set, or smaller than the smallest number. This is useful for weighted average problems: if you average the weights of 6 cats that each weigh 10 pounds, and 8 dogs that each weigh 30 pounds, the result will be somewhere in the middle in between 10 and 30. The more evenly spread the numbers are, the closer the average will actually be to the middle. 
• Only use a Venn diagram for rare “3-group” overlapping set problems. For almost all overlapping sets, the Overlapping Set Matrix is quicker and easier. 
• You’ll sometimes see rates problems that look like this: if it takes four people twelve days to sew eight jackets, how long does it take ten people to sew ten jackets? A quick trick for approaching these is to start with the original statement, and then “scale” it upwards or downwards. Here’s what that might look like: 

It takes 4 people 12 days to sew 8 jackets.

1 person will take 4 times as long to do the same amount of work, so it will take 1 person 48 days to sew 8 jackets. 

If that 1 person sews ⅛ as many jackets, it will take ⅛ as many days. So, it takes 1 person 6 days to sew 1 jacket. 

If a person takes 6 days to sew a jacket, then it will take 10 people 6 days to sew 10 jackets (one per person). The answer is 6.

Fractions, Decimals, and Percents Tips

• When a fraction has zeroes on the end of both the numerator and the denominator, chop off the same number of zeroes from each (just make sure you count carefully!). 1,000,000 / 5,000 simplifies to 1,000 / 5. 
• Likewise, if a fraction has decimals in both the numerator and denominator, you can simplify by moving both decimal places by the same amount and in the same direction. For instance, 0.0007 / 0.14 = 0.007 / 1.4 = 0.07 / 14 = 0.7 / 140 = 7 / 1,400. 
• Use this technique to directly translate percent problems from English into math without having to convert between decimals and percents. 

Working with Numbers Tips

• You can use a similar ‘scaling’ technique to calculate percents, fractions, or decimals. For instance, if you want to find 0.1% of 50,000, start like this: 

10% of 50,000 is 5,000.

So, 1% of 50,000 is a tenth of 5,000, or 500. 

So, 0.1% of 50,000 is a tenth of 500, or 50. The answer is 50. 

• To quickly divide a number by 5, divide it by 10 first, then multiply by 2. For example, 1,880/5 = 1,880/10 * 2 = 188 * 2 = 376. 
• Arithmetic can be easier if you “split up” or rearrange the numbers before you do the math. Suppose that you need to calculate 117 – 98. Rewrite this as 117 – 100 + 2, or 17 + 2, which equals 19. 
• Use a similar technique to quickly calculate the square of a number that’s close to an easy value.

79² = (80 – 1)² = 80² – 2(80) + 1 = 6,400 – 160 + 1 = 6241

• To find a good common denominator, think of a value (if there is one) that both numbers are divisible by. Divide one of the two numbers by that value. Then, multiply that by the other number. 
  • For example, to find a common denominator between 25 and 15, note that both are divisible by 5. So, divide 25 by 5, which gives you 5, then multiply that by 15, giving you 75. 75 would be a good common denominator.
• It can be useful to memorize the approximate square roots of 2 and 3: √2≈1.4 and√3≈1.7. To remember this, at least if you’re in the US, think of two dates: Valentine’s Day is on 2/14 and St. Patrick’s Day is on 3/17. 
• To estimate other square roots, think of a perfect square that’s as close as possible to the value you’re dealing with. (You have your perfect squares memorized, right…?) Estimate based on that—so, for instance, √79 is a bit smaller than √81, which equals 9. 

What to Memorize for GMAT Quant 

Below are 4 tips to help you strengthen your mental math on the GMAT.

GMAT Mental Math Tip 1:

What: Times tables up to 12 (and practice your multiplication and division in general)

Why: You’ll be doing these calculations so often during the test that errors will destroy your score and cost you time. When my students complain that they make too many “silly mistakes,” one of the first things that I ask them is, “What’s 12 times 7?” If you can’t answer that quickly, then not only have you identified the problem, you’ve also learned that the solution to your problem is a relatively low-effort one.

How: (1) Make flashcards! And don’t use a flashcard app; there’s some evidence that writing the flashcard yourself will help you memorize it. (2) There are endless opportunities in everyday life to practice your times tables: my suggestion is to just stop using your calculator when your brain will do. Need to buy eight pizzas at $9 each for your little sister’s soccer team? Figure out the total in your head. Need to split that total among 6 team parents? Put that calculator app away, cheater – you can do that on your own now! Got an option to pay your car insurance in a lump sum vs. 12 monthly payments? Figure out how much more the monthly option is going to cost you. Bored at the gas tank? Check your odometer at two fill-ups in a row, and figure out what kind of mileage your car actually gets (vs. what the slick car ad copy promised). There are endless opportunities out there as long as you stay curious.

GMAT Mental Math Tip 2:

What: Fraction-percent conversions for 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/10, 1/20, and 1/100.

Why: Because these conversions lead to many other conversions (for example, 1/9 is 11.1%, so 7/9 is 77.7%). Also, a problem that is difficult in decimal/percent form can become infinitely easier in fraction form, and vice versa. Want proof? What’s 37.5 percent of 560? Easy: it’s 3/8 of 560. So divide by 8 to get 70, then multiply by 3 to get 210.

How: Remember that pizza for your little sis? What’s the delivery charge going to be if you want to give the delivery person a 15% tip? (Just take 1/10 of the total, then half of that, and add those two numbers together). Want to buy that flat screen TV at Costco, but worried about the 9% sales tax? Just divide the price by 11 and tack it on. Here’s one of my personal favorites: every time you see some item on sale for some percentage off, figure out what it actually costs, and then immediately find something else that you wanted recently that you could buy at full price for roughly that same amount of money. Then you’ll know whether you’re really getting a deal. Oh, also: tip charts are the new answer keys. Figure out the tip yourself first, then check to make sure you’re right!

GMAT Mental Math Tip 3:

What: Prime numbers up to 100

Why: Because most big numbers are just a bunch of smaller prime numbers multiplied together. I saw a GMAT problem where a crucial final step was to add 1/15 + 1/18. Far too many of my students thought that they needed to convert the denominator to 270. But the ones who found prime factors of 15 (3 × 5) and 18 (2 × 3 × 3) noticed that both 15 and 18 contain a 3, so 90 is actually the common denominator; those students, on average, solved the problem about a full minute faster. Also, some GMAT problems ask you quite directly whether a number is prime. Why not just memorize some primes in advance?

How: For all positive integers from 2 to 100, a number is prime if it’s not divisible by 2, 3, 5, or 7. So just start learning primes in the shower; see if you can get to 100 without missing any. Conveniently, this will also teach you shortcuts for how to check whether a number is divisible by 2, 3, or 5 (there’s no great shortcut for 7, so see “times tables,” above!).

GMAT Mental Math Tip 4:

What: Powers of 2 (2, 4, 8, 16, 32, 64, 128, 256, 512)

Why: Because you’ll need to be able to recognize them on sight, not to mention that it’s important if you want to keep the respect of your IT team. The GMAT and GRE will ask you to simplify expressions like 32^5 · 64^3. This is impossible without knowing that 32 is 2^5, and 64 is 2^6.

How: Do a web search for “2048” – it’s a surprisingly addictive web-based game; if your boss catches you playing at work, don’t say I didn’t warn you.

Honorable Mention Tips:

Learn the two most common Pythagorean Triples (3-4-5 and 5-12-13), the ratio of sides in a 45-45-90 triangle and a 30-60-90 triangle, the decimal approximations (to a tenth) of √2, √3, and π, powers of 3 (notice I said “powers,” not “multiples”), factorials from 2! to 6!, and how to factor the difference of squares. If you show up to the first day of my GMAT class with everything in this post down cold, I promise it will not only enrich your experience in class, it will also help you achieve the best score possible.