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  GMAT "Tricks" Part 1: Backsolving

Posted by ian on Fri 05 Sep 08 at 12:25am

GMAT 'Tricks' Part 1: Backsolving

This will be the first in an occasional series analyzing the value of the GMAT 'tricks' most often mentioned in test prep books and courses.

Many test prep companies advertise 'tricks' that will, they claim, enable you to use the structure of the test to your advantage. This sells books- many GMAT test-takers no doubt hope that there are some simple 'secrets' to doing well on the test, secrets they might learn about from a test prep book or course. Some of these 'tricks' are more useful than others, of course. We'll look at the most popular of these, and break down just how useful these 'tricks' really are.


The idea behind 'backsolving' is simple. Each GMAT Problem Solving question has five answer choices. In some questions (mainly algebra and word problem questions) you might be able to plug the answer choices into the question to see which answer works. An example (this question is much easier than real GMAT questions, but is useful for illustration):

If 2x - 3 = 5, what is the value of x?
A) -1
B) 2
C) 3
D) 4
E) 5

We could start by testing answer A, for example: if x = -1, then 2x - 3 = 2(-1) - 3 = -5. That's not equal to 5, so A is the wrong answer. We could continue to do this with each answer choice until we found the correct answer.

I'm sure it's already clear why backsolving is not a great idea for this question. For each answer choice you try, you end up solving the problem once. You might end up doing all the work of solving this problem four times if you're unlucky enough not to find the right answer until your last attempt. If we solve algebraically, we only do the work once:

2x - 3 = 5
2x = 8
x = 4

And this is very often the case on the GMAT: backsolving wastes time. If you can see how to do a question conceptually or algebraically, it will almost always be faster. If you can't see how to do a question directly, then you may be able to fall back on the backsolving strategy, but it will not normally be the best strategy. In addition, in most cases backsolving only lends itself to word or algebra problems with numerical answers, and you won't see many of those past the medium difficulty level of the GMAT; it's not a strategy that will help you boost a 75th percentile score into the 90s.

Often books that advertise this strategy also include questions which are only convenient to solve by backsolving. What matters, of course, is the real GMAT. We looked at real (retired) GMAT questions: the last 50 questions (numbers 200-249) in the 11th edition of the Official Guide, the hardest Problem Solving questions in the book. Of these 50 questions:

14 questions could, in theory, be solved by backsolving;
the only question where backsolving seems a good approach is number 200, and even there, the algebra is simple: the time required is equal either way.
Someone stuck on question 223 might backsolve, but this is such a common question type that a well-prepared test-taker should have a much quicker strategy here (subtract the speeds);
Question 228 can be backsolved, but the answer choices are the only plausible answers, so seeing them is not very helpful;
Question 232 can be backsolved, but the algebra is very fast (clear the denominators);
On questions 205, 210, 211, 213, 220, 222, 235, 237, 238, and 240, if you choose to backsolve, you are spending more time than you should. In these questions, if you backsolve, then for each answer choice you need to test you are doing the same steps (in reverse) as you would do if you solved the question algebraically. The algebra gives you the answer on the first try, while by backsolving you may need to do the same question several times over. Worse still, on some questions this can lead to very time-consuming calculations (213 and 238, among others).

You'll have about 20 Problem Solving questions on a GMAT. If the sample from the hardest questions in the Official Guide is representative of the real GMAT, you could, in theory, backsolve about 6 of these. However, it's only a time-neutral strategy on between 2% and 6% of Problem Solving questions. That's between 0.4 and 1.2 questions on a real GMAT. It was not time-saving on a single question.

So, if you're doing well on the GMAT, and therefore seeing difficult questions, it may be worthwhile using backsolving as a fallback strategy for when you don't see a conceptual or algebraic approach, but there will almost always be a better strategy available. Even if we don't use backsolving, we'll look at it again in a future post: if you're going to use it, we'll explain how to use it properly.

[I posted an earlier version of the above to the Beat the GMAT forum]



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