When confronted with a GMAT problem that features numerous variables or unknowns, in which you are not asked to directly solve for any of the unknowns, picking numbers for those unknowns is one of the most effective ways to solve the problem.  One particular type of problem in which you should almost always pick numbers is percent problems featuring unspecified values.  For example:

Sample problem:

In 1998, the profits of Company N were 10 percent of revenues.  In 1999, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues.  The profits in 1999 were what percent of the profits in 1998?

Unspecified value percent problems are questions in which every number in the problem is either a percent or ratio.  Remember that if even one number in the problem cannot be expressed as a percent, you will not be able to pick numbers to solve.

However, when you can express every number as a percent, then picking numbers will be the best option available.  And here is the most important piece of this technique to remember: when picking numbers on percent problems, you should almost always pick 100 as your unknown value.  Because a percent is always out of 100, by setting 100 as your initial number, you will be directly working in percents from the beginning.  Then, when you get to the end of the problem, you will already have you answer in percent terms.  And of course, it’s much easier to figure out, say, “17.2 % of 100″ than it is to find “17.2 % of 68″, or another random number, so keep the math easier on yourself.  Sticking with 100 saves time and brain power overall.  (See our post on Picking the Right Numbers for ideas on what to pick for other types of problems.)

When picking numbers in percent problems, it is still important to remember the percent formulas, in order to double-check your work.  Make sure to keep in mind that percent equals final/original x 100 (or part/whole x 100) and percent change equals (difference/original) x 100.

By following this strategy you will be well on your way to answering percent problems quickly and effectively.  For more examples of this type, view our Kaplan GMAT Video on Percents in the Answer Choices.

Here’s the solution to the sample problem we included above:

In 1998, the profits of Company N were 10 percent of revenues.  In 1999, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues.  The profits in 1999 were what percent of the profits in 1998?

Since we have a percents question with an unspecified value in the question stem, we can pick numbers, and we should pick 100.  Pick 100 for the 1998 earnings.  That means profits were 10 (10% of 100).  Revenue in 1998 was 80 (since it fell 20%),  and profits were 15% of that revenue, or 12.

The question becomes, 12 is what percent of 10?  Or 12/10 x100 = 120% (which is the correct answer here).

If you read Adam Grey’s March 12th post on Yes/No Data Sufficiency questions, you learned how to pick permissible numbers in order to determine sufficiency.  In effect, you are trying to prove insufficiency by picking one permissible number that yields a “Yes” and one that gives a “No.”

The next logical question is, How do I know what numbers might yield a different result?  If you don’t have a strategic approach, you could end up picking several numbers that all yield the answer “Yes” and make a hasty decision that a statement is sufficient.  Even if you do eventually find the right numbers, you waste valuable time if you are picking randomly.  On the GMAT, we have to pick numbers strategically.

Let’s take a look at some specific examples:

Is x odd?

(1)    x/2 is not an integer
(2)    2x + 3 is odd.

When I elicit permissible numbers for Statement (1), students often give me numbers like 3, 5, and 7.  Sure enough, all of these produce non-integers when divided by 2, and all are odd, so students lean towards sufficient.  But wait!  Who said x had to be an integer?  Certainly a number like 6.4289 would yield a non-integer when divided by 2, so it’s permissible, and it’s not odd.  Sometimes Yes, Sometimes No:  Insufficient!  Similarly, we have to recognize that odds and evens are both permissible for Statement (2), and therefore Statement (2) is insufficient.  [By the way, put the statements together and you'll find that (C) is correct.  See why?]  So we have to consider odds vs. evens and integers vs. non-integers in such number properties questions.

Let’s look at another one:

Is x negative?

(1)    X^2 +25 = 89
(2)    X^3<x

Whenever we see exponents, we have to fight the temptation to assume that our variable is a positive integer.  Remember that when exponents are involved, negatives and values between 0 and 1 are special.  For statement (1), which simplifies to x^2 = 64, we have to remember that positives and negatives “go positive” when squared.   Since 8 and -8 are both permissible, we don’t have sufficient information to determine whether x is negative.   For Statement (2), positive integers (such as 4 or 6) aren’t permissible cubing increases the original numbers.  But let’s try different kinds of numbers.  A negative number such as -2 will produce a situation in which x^3<x, so x could be negative.  But don’t forget about, say, 1/2.   That produces a smaller number when cubed as well!  So x could be positive.  Insufficient.

Combine the information, and you’ll see that there is only one permissible number, -8, so the answer is (C).   An exponent is a great trigger that tells us to consider the impact of special numbers.
But let’s say you look a problem and you know that you need to pick different kinds of numbers, but you don’t know which numbers will be important.  Do I need to consider negatives here?  What about non-integers? Well, here is a list of seven numbers that help us cover our bases and stay strategic (with thanks to expert Kaplan GMAT teacher Adam Maze!):

-2, -1, -1/2, 0, 1/2, 1, and 2.

Think about it.  In these seven numbers, you have: odds and evens; positives and negatives; integers and non-integers; and a very important number, 0.

The moral here: we need to try different kinds of numbers: odds and evens, positives and negatives, integers and non-integers, greater than one and less than one, big numbers and little numbers.  Now, for any given problem, some of these categories might be relevant for determining sufficiency, but others won’t.  With practice, you’ll be able to identify what issue really matters, and you’ll have a strategic approach to picking numbers.

As you’re preparing to take the test, you become very familiar with numbers, and I don’t mean just the numbers within the quantitative question.  Can you recognize the significance of the following numbers?

1) 700

700 is a 90th percentile score.  The average GMAT score for top 10 b-schools is right around the 700 range, so it’s a good score to set as your target if you’re looking to attend any of those schools.  If you knew this, that’s great.  You’ve probably already started looking at business programs you’re interested in.  If you haven’t already, it’s a good idea to take a practice test to see what range you’re scoring in and how far you have to go to reach your target score.

2)  75/37

75/37 refers to the GMAT quant section being 75 minutes long and containing 37 questions.  In this handy format, it reminds you that you have an average of 2 minutes per question.  If you knew this, you’ve probably cracked open some prep material and you might even be cognizant of time management being a crucial skill for GMAT success.

3)  8

8 is the number of minutes for each of the two breaks you’ll have on the GMAT.  The first of the eight-minute breaks will be after the Analytical Writing Assessment section, and the second will be after the Quantitative section.  If you knew this, you may already be engaged in some intense preparation and have completed a practice test as well.

You may be thinking “I care about hitting a 700, and it’s good to know the 75/37 thing, but why do I care about 8?”  The best test takers are those who utilize every minute of the exam to maximum efficiency.  During the breaks, you need to stretch your legs, clear your head, and get yourself pumped up for the next section.  Lastly, for the breaks remember that 6.5 = 8.  If you exceed the eight minutes, the test will start again, with or without you!  So what I always tell students is to think of the 8 minute break as a 6.5 minute break.  You want those extra few seconds as a buffer before starting again; otherwise, what you did to relax during the break is negated by the fear of “did the test resume already?!”