The Perils of Picking Numbers
February 05, 2008
Just about every GMAT Preparation company, along with nearly every GMAT book on the market, teaches some version of a strategy called "picking numbers." Every company has a different name for it, but the technique is the same: given an abstract problem with a bunch of variables in it, start substituting real numbers for the variables.
The advantages of picking numbers are obvious, and that's why nearly everyone teaches the strategy. Once you've chosen values, the problem is much easier. Rather than a rate of k kilometers per h hours, you can work with a rate of 120 kilometers per 2 hours, or 60 miles per hour.
On Data Sufficiency, picking numbers is also popular, especially for Number Properties items, questions involving topics such as factors, multiples, evens, odds, primes, and remainders. Again, it is useful in that it makes abstract problems concrete, and thus brings makes some tough questions down to a level where more people can handle them.
Why You Should Stop
There are many reasons why I almost never pick numbers, and rarely recommend that my students do so.
The first is that it puts a ceiling on your potential GMAT Quant score. On easy- and medium-level questions, picking numbers is magic. You plug in some numbers, do some calculations, and there it is: you've got an answer, and you didn't have to do a single abstract step. But as questions get harder, the same strategies stop working. The question becomes too involved; it might be complicated just to decide which numbers to pick in the first place; or more than one answer choice will appear to be correct.
Picking numbers is effective on a certain level of straightforward question, but it's very hard to do better than a 60th or 70th percentile Quant score if you heavily rely on the strategy. One reason for that is that the makers of the GMAT know about these strategies: I know from personal experience that it's easy to write a question to make picking numbers difficult, or to reward test-takers who avoid the strategy altogether.
You Should Learn the Math
Every question you will ever pick numbers on can also be handled algebraically. Personally, I do 99% or more of GMAT questions algebraically, and in most cases teach my students to do the same.
Every time you opt for picking numbers, you are practicing elementary arithmetic, when the question is really dealing with algebra or number properties. The same concepts will be tested in questions when you can't pick numbers. If you've practiced those types of questions in a more abstract fashion, you'll be able to handle questions in different forms. In my Total GMAT Math, I focus on the skills you need to answer those questions, not strategies that limit your understanding of the material.
This brings us back to the first issue I mentioned: Picking numbers puts a ceiling on your score. It prevents you from practicing techniques you'll need to use on other questions. At the very least, even if you are committed to picking numbers, spend some time redoing those questions with another method.
DS questions are where students tend to pick numbers the most, and it is where picking numbers requires (and often wastes) the most time. Again, picking numbers is used as a way to avoid doing the math, when sometimes the mathematical techniques required really aren't that difficult.
Let's try an example, based very closely on an example in The Official Guide:
Is n an odd number?
(1) 2n is an even number.
(2) When n is divided by 2, the result is not even.
Many people see a question like this, jump into the statements, and start picking values of n that make each of the statements work. Eventually you can get an answer, but it's very hard to prove that a statement is sufficient by picking numbers: You can keep choosing new values all day long, but if you're just plugging in number after number, you'll never be 100% sure that you haven't ignored one key value that gives you the opposite answer.
By contrast, try this algebraically. Statement (1) is insufficient. An even number is a number that is 2 times an integer: call it 2i. So, (1) says that 2n = 2i, or that n = 1. In other words, we know that n is an integer. Could be even, could be odd.
Statement (2) is also insufficient. Again, an even number is twice an integer, so we can simplify the statement to an equation ("!=" means "not equal to"):
n/2 != 2i
Multiply both sides by 2:
n != 4i
4i is the same as "4 times an integer," which is another way of saying "a multiple of 4." So, n is not a multiple of 4. n could be even, it could be odd, and it could be a non-integer.
Taken together, the statements are still insufficient. In both statements, it was possible that n was even (as long as it wasn't a multiple of 4) or odd. Choice (E) is correct.
At this point in your GMAT Prep, the explanation I just gave might seem very complicated. It takes a bit of getting used to, but I can assure you that, as questions get harder and you spent more time practicing abstract approaches to questions, this saves you an enormous amount of time over picking numbers. There are several chapters in Total GMAT Math that focus on approaches like these to just about every type of number properties question you'll face on the GMAT.
It's OK, Sometimes
I'll admit, there are limited cases where picking numbers is an acceptable last resort. I've been known to do it occasionally, even on the GMAT itself. But consider other alternatives first. And when you are practicing, if you pick numbers the first time you try a problem, do it again more abstractly.
It's great if you know how to do it one way, but it's even better if you can do it multiple ways. You never know what variations the GMAT will introduce to these question types, and sometimes those variations make one method more effective than another.
About the author: Jeff Sackmann is a GMAT tutor based in New York City. He has created many resources for GMAT preparation, including the popular Total GMAT Math and Total GMAT Verbal, as well as 1,800 practice GMAT math questions.