GMAT Strategy: Comb That Perm!

Statistics questions can be some of the most exasperating Quant questions on the GMAT. And among those, Combination and Permutation questions may just be some of the worst. The good news: statistics questions are some of the least frequently tested concepts on GMAT Quant. The bad news: you’re still likely to see at least 1 Comb-Perm question come test day. Because higher scorers will likely see a difficult Comb-Perm question, strategies to tackle them are needed. That being said, don’t let those tricky Comb-Perm questions make you want pull your hair out. Often times, there’s an easier way to smooth over those Comb-Perm cowlicks (sorry, I’ll try to reign in the hair jokes).

Harder questions on the GMAT are all about reasoning ability and critical thinking. For difficult Comb-Perm questions, the key is properly adapting the typical method of solving these questions. To wit, we present Comb-Perm: Front-to-Back or Back-to-Front.

Let’s take a look at an example:

If from a certain class of 10 children, 4 children will be chosen to form a committee, how many different committees can be formed where Adam and Miles are not on the same committee?

(A) 56

(B) 84

(C) 112

(D) 182

(E) 336

Now, let’s take a look at the straight forward, or Front-to-Back Method, to solving this question. Essentially, this method requires identifying the number of possible combinations for the committee for EACH of the variations that would satisfy the criteria (namely, that Adam and Miles can’t be on the committee together).

So, the three ways to satisfy the criteria:

- Adam on the committee but not Miles.

- Miles on the committee but not Adam.

- Neither Adam nor Miles on the committee.

Now that we have the three possible variations that satisfy the criteria, we can determine the number of possible combinations for each:

Thus, the total possible number of combinations = 56 + 56 + 70 = 182.

With this approach, it is imperative that you see all three variations. If you overlook one (or more), you get the incorrect answer. For many, it is difficult to visualize the variations that would allow one to calculate the correct answer on such problems.

However, if you have an alternative approach, your chances of correctly answering difficult Comb-Perm problems (and all problems) goes up!

Enter the alternative, or Back-to-Front, method:

- Find the total number of possible combinations.

- Find the number of combinations that VIOLATE the criteria (i.e. Miles and Adam together).

- Subtract the two.

Thus, the total number of possible combinations: 210 – 28 = 182.

So we can see that we get the same answer with different approaches. Most problems have multiple methods by which you can solve. Here, finding the more easily identifiable combinations allow us to more safely (and effectively) calculate the correct answer.

The GMAT, at base, tests higher order thinking skills. One of those skills is having alternative methods at your disposal to work around roadblocks. The methodology we employed here can be used to similar effect on a wide variety of GMAT questions, from complicated Geometry based on shaded or overlapping figures, to quadratic equations, to complex probabilities. The principle: find the quantities you know, see if you can manipulate those to find the solution you need.

Until next time, good luck with all your GMAT preparation!


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