GMAT Gurus Speak Out: Avoiding Careless Math Errors

We’re back with the next installment in an occasional series on the Veritas Prep Blog, called “GMAT Gurus Speak Out.” Veritas Prep has dozens of experienced GMAT instructors around the world (all of whom have scored in the 99th percentile on the GMAT), and it’s amazing how much collective experience they have in preparing students for the exam. This new series brings some of their best insights to you. Today we have another installment from Valerie Browning, a Veritas Prep GMAT instructor in Houston.

The easiest place to mess up a problem is in the “careless error” department. The more math we grind out on a page, the more opportunities we have to make a transposition error or an addition error or a basic math error of some other sort.

Almost all my students have been surprised at how much math they actually can complete mentally instead of writing it all out longhand. It’s amazingly accurate to do some of these calculations in your head once you have a few tools to use.

Let’s take a look at one of my favorite techniques for multiplication…

If we have something like this:

15 * 120

there are several ways we can go about it.

First, we can factor it, and there are several different ways to do that:

We can break the 15 into 10+5:

15 * 120 = 10*120 + 5*120 = 1200 + 600 = 1800

OR

We can break each piece into factors:

15*120 = 15 * 12 * 10 = 15 * 2*6 * 10 = 15*2 * 6*10 = 30 * 60 = 1800

But even easier, in many cases, we can use something called the “double and half” method.

We double one term in the problem, and half the other one. Then complete the multiplication using these new numbers.

Take 15 * 120 for example. Let’s double the 15 and make it 30. That means we need to half the 120 and make it 60.
So instead of having 15 * 120, we have 30 * 60, which is 1800. Easy peasy.

You may be wondering why this works… This works because if we have x * y and we make x into x/2 and we make y into 2y, then we now have x/2 * 2y which is still xy. The 2’s cancel.

This is ok with variables, but it can be really powerful with numbers:

Let’s look at another one:

5 * 1500.

You might recognize 5 * 15 as 75, in which case this isn’t too bad, but we can also double the 5 and half the 1500.

That means we now have 10 * 750 which is 7500. Any time you have 5 times something, we can make the problem into 10 times half of something. It’s often MUCH quicker!

Double and Half is particularly useful when we have something like 1.5 * 250. Let’s double the 1.5 and make it 3. (That’s MUCH easier to manipulate!)
Next, let’s cut 250 in half and make it 125. Now we have 3 * 125. This is 375. (Multiply 100 by 3 and then multiply 25 by 3 and add the results if you want to do this part in your head, too).

Let’s try another couple of these:

7.5 * 30 becomes 15 * 15, which is one of those squares you memorized back in the Arithmetic lecture, and it’s 225.

5 * 18. You might be able to do this one a couple of ways – but if we make the 5 into a 10 and make the 18 into a 9, we have 10*9, which we can ALL see is 90.

3.5 * 8 becomes 7 * 4 which is 28.

2.5 * 50 becomes 5 * 25 which is 125.

Happy multiplying!

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