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.