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The Top 5 Strategies for GMAT Problem Solving (Part 1)

Today’s GMAT article comes from Manhattan Review Asia, a provider of GMAT Prep courses in Hong Kong, Kuala Lumpur, Manila, and Singapore, among others. In this article, they reveal Manhattan Review’s best 5 strategies how to tackle GMAT Problem Solving questions. In fact, the article is so detailed that we had to split it into two parts.

As with every type of question on the GMAT, the biggest challenge to answering Problem Solving questions is figuring out how to get to the right answer in the minimum amount of time. If we had half an hour for each question, we would all be scoring in the 99th percentile. We don’t have half an hour. So forget pride. It doesn’t matter how good you think you are at math. If you can get to the right answer without crafting elegant equations doing fancy algebra, go for it! At some point in the test, a question will stump you. That’s when you’ll be thankful for all of those precious seconds you saved by skipping elaborate calculations. Here are five tips on how to improve your Problem Solving skills and have fun on the test:

1. Go slower in order to go faster

It is absolutely essential that you take the time to read the question very carefully. Don’t make assumptions; don’t jump to conclusions; don’t take it for granted that the question is asking the same thing as similar questions asked you in the past. Draw a diagram; write out as clearly and as free of confusion as possible who did what in the past and who is doing what at the moment. It may seem as if you are losing time, but you are not. You are saving yourself precious minutes that you would lose by failing to read the question properly and answering what you haven’t been asked. The strategy is: Get the right answer on the first try, not on the fourth try. Before test-day, practice sketching problems out.

2. Avoid traps

The most frequent complaint I hear from students as they start to prepare for the GMAT is that the math they have to do is so basic, yet so difficult. Why should they have to go back in time and sweat over problems that they used to polish off effortlessly in sixth grade? This lament is misconceived. The math in the GMAT is not like the math you did at school. To be sure, GMAT math isn’t especially advanced. However, it is extremely tricky and there is a good reason for that. The GMAT tests your ability to make logical inferences, to extract important information from a confusing mélange of data and to perform mathematical operations quickly and without a calculator. Above all, you have to be aware at all times that the test-givers have set any number of traps for you to walk into. No matter how skilled you are at math and no matter how much calculus you may have studied in the past, you can fall into a trap as easily as any novice.Here is an example of a reasonably straightforward problem that many people get wrong because they make the very mistake that the test-givers expect you make. The question comes from the Manhattan Review Study Companion:

Two secretaries, Sally and Lisa, type at even but difference paces. Sally is more experienced and types 80 characters per minute. Lisa, a beginner, can type only 30 characters per minute. On one day, Lisa starts typing before Sally. At some point, both have typed the same number of characters. Then both continue typing and Sally types 800 more characters until her computer breaks down. Assuming Lisa does not take any break, how long, in hours, will it take her to finish typing the same number of characters?

(A) 53/180
(B) 4/9
(C) 13/18
(D) 15/23
(E) 5/18

Let’s set the problem out. Lisa starts typing before Sally does. Sally catches up and then overtakes Lisa. Sally types another 800 characters and stops. How long will it take Lisa to catch up with Sally?

First trap: The easiest mistake to make is to get bogged down on issues that we are not concerned with. Everything that happens before Sally overtakes Lisa is irrelevant. We don’t need to know what time Lisa started, what time Sally started and how much time elapsed before Sally overtook Lisa. We need to focus on what is being asked and not lose time trying to find answers that we don’t need and can’t find. All we need to concern ourselves with is how long it will take Lisa to be where Sally was before she stopped typing.

And now the second trap, the one that almost everyone falls into: Perfectly reasonably, we assume that Lisa will catch up once she’s typed the 800 characters that Sally had typed. The arithmetic is pretty straightforward: Lisa types 30 characters per minute. She needs to type 800 words. This will take her 800/30 minutes or—since they want the answer in hours—800/30 x 60 hours.

800/1800 is 8/18 or 4/9 hours. So we happily answer (B) and move on.

But (B) is wrong. We walked into the trap of assuming that while Sally was typing her 800 characters, Lisa was just twiddling her thumbs and that she only began typing when Sally stopped. That’s wrong. There is nothing in the question to suggest that Lisa at any time stopped typing. While Sally was typing those 800 characters, Lisa continued to type. Therefore, it wasn’t 800 characters that Lisa needed to type to catch up. Lisa needed to type 800 characters less the characters she typed while Sally typed those 800 characters.

Since Sally’s typing rate is 80 characters per minute, typing 800 characters should have taken her 10 minutes. During those 10 minutes Lisa, whose typing rate is 30 characters per minute, typed 300 characters. Therefore, Lisa only needed to type 800-300 or 500 characters to catch up. That should take her 500/30 x 60 hours. 500/1800 = 5/18. And the correct answer is (E).

As you can see, the arithmetic in this problem is very simple. The hard part is figuring out exactly what they are asking and avoiding making fallacious assumptions.

3. Make it easy on yourself

The GMAT questions are often confusing. The issues are presented in such a way that you really have very little idea as to what is going on. At school, math problems were crafted meticulously, precisely in order to ensure that there is no confusion or ambiguity. The GMAT isn’t like that. The problems you have to solve are not unlike the ones you deal with in everyday life. Somebody writes something in a memo and doesn’t bother to check whether the information is confusing and the question is ambiguous. In the GMAT, you have to accept what you are given. You can’t request clarification.So what to do? If you’re not sure what the information means or what the question is asking, try a simpler example. Try restating it for yourself. What would the information mean if it related to something you’re far more familiar with? If you read it somewhere other than at a GMAT test center, what would you understand it to mean? Take a look at the following problem. It too comes from the Manhattan Review Math Study Companion:

A certain shoe store pays special attention to stocking shoes of sizes 8, 9, 9.5, and 10. It stores 1/3 as many shoes of size 10 as those of size 8, and ½ as many shoes of size 8 as those of size 9. If the shoe store stocks equal numbers of shoes of size 9 and 9.5, what percent of shoes in the store accounts for shoes of size 8?

(A) 10%
(B) 12.5%
(C) 15.25%
(D) 18.75%
(E) 20%

The information is presented in a confusing fashion. What exactly does “1/3 as many shoes of size 10 as those of size 8” mean? Does the store have three times as many size 8 shoes as size 10 shoes? Or vice-versa? The answer isn’t obvious. Try expressing the information in another context. “Sally has 1/3 as many pieces of candy as Robert.” Now it’s much clearer: Robert has three times as many pieces of candy as Sally. Armed with this insight, we can now make sense of the situation in the shoe store. There are three times as many shoes of size 8 as there are of shoes of size 10. And there are twice as many shoes of size 9 as there are shoes of size 8. If the information had been phrased like that, the question would have been easy to answer. But then it wouldn’t be the GMAT.

Let’s now solve the problem. The easiest way to do this is to use hypothetical numbers. We have 1/3 of one thing and 1/2 of something else. Let’s say there are 20 size 10 shoes; therefore, there must be 3 x 20 = 60 size 8 shoes.

There are twice as many size 9 shoes as size 8 shoes. Therefore, there are 120 size 9 shoes. And there are 120 shoes of size 9 ½. Altogether therefore there are 20 + 60 + 120 +120 =320 shoes. So what percentage of the shoes in the store is comprised of size 8 shoes? The answer is 60/320 x 100 = 18.75%. The answer therefore is (E).

Stay tuned for the second part of Manhattan Review’s best 5 strategies for GMAT Problem Solving. In the meantime, you can start practicing for the test immediately by taking a free GMAT practice test at the Manhattan Review website.