Break Glass in Case of Emergency

The strategies we’re going to outline for you in this chapter are often misunderstood by students. It’s not that the concepts are overly difficult or foreign. In fact, they rely mostly on straightforward logical reasoning and simply paying close attention to the problem.

However, many students believe that these strategies are a one-stop shop for GMAT success. This is emphatically not the case.

When you are confronted with a GMAT math problem, your goal should be to solve the problem using the math concepts and strategies covered in this book. Solving the question should be your goal every time a new math question appears on your screen. You should take an internal inventory of the question—determine the kind of math being tested, the possible steps for completing the problem, the information provided by the problem—and then you should reach into your math toolkit to pull out the appropriate tools to solve the problem.

So, these POE strategies are not a silver bullet to solving math problems. They should not be your first resort.

These strategies should be considered an emergency valve. They are a rip cord for you to pull when you need it the most. That usually means that you are either stuck—the solution isn’t working out—or that you are running out of time.

Hard Questions

Unless you are a truly masterful mathematician, or for some reason the adaptive portion of the GMAT testing algorithm is broken that day (hint: it won’t be), you will eventually run into a math problem that you don’t know how to solve. What do you do? Spending a lot of time hammering away at a problem is not necessarily the best idea, as you have other problems that you need to work on that may be easier to solve. So, you decide to guess and move on. That’s a good idea!

But wait! Before you make a blind guess, take a second and apply the POE strategies outlined in this chapter to see whether you can eliminate any answer choices. You may still need to guess but your odds of guessing correctly will be greater if you’ve already eliminated some answer choices. This way, you have the best possible chance at answering an additional hard question correctly, which will improve your score.

Running Out Of Time

Let’s say you’re nearing the end of the allotted time for the Quantitative section and you look up only to realize that you have more questions left than you have time to work on. You know it’s in your best interest to click on an answer for all the questions on the test, so you decide to guess on the remaining questions.

But wait! Don’t guess blindly. Try some of these POE strategies for these remaining questions. If you can eliminate some answers before you guess, great!

Let’s Get to Work

Now that we’ve established when you should use these POE strategies, it’s time to discuss the actual strategies. For the remainder of this chapter, we are going to assume that you have already tried to answer the question using math concepts and that you were unsuccessful. Or, that you are running out of time and need to make quick, educated guesses about the answers. You are ready to break the glass and use your emergency tools. But what are those tools and how do you wield them?

Take a look at the following question. Using the knowledge you gained from Chapters 4 and 5, are there any answer choices that you can eliminate using POE?

Twenty-two percent of the cars produced in the United States are manufactured in Michigan. If the United States produces a total of 40 million cars, how many of these cars are produced outside of Michigan?

8.8 million

18 million

31.2 million

48.8 million

62 million

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Ballparking

Let’s see if we can eliminate any answer choices from this problem quickly and without doing any heavy lifting. The problem is asking for the number of the 40 million cars produced in the United States that are produced outside of Michigan. The problem also states that 22 percent of the cars produced in the United States are produced in Michigan, so you know that 78 percent of the cars produced in the United States are produced outside of Michigan. Even if you’re unfamiliar with percentages, are there any answer choices that could be easily eliminated using this information? Well, if there are only 40 million cars produced in the entire United States, is it possible for any combination of states outside Michigan to produce more than 40 million cars? No, it’s not, so (D) and (E) can be eliminated because they are greater than the total number of cars.

This tactic is called Ballparking. Ballparking usually involves either making rough comparisons of numbers or rough estimates of the size of an answer. In this case, comparing the answer choices to the total number of cars produced, which is stated in the problem, eliminates two answer choices.

Are there any other answer choices that can be eliminated using Ballparking? Let’s try a rough estimate of the size of the answer. If 78 percent of the cars produced in the United States are produced outside of Michigan, then you know that more than three-fourths of the 40 million cars produced in the United States are produced outside of Michigan. Three-fourths of 40 million is 30 million. Two of the answer choices, (A) and (B), are less than half of the total number of cars produced in the United States. Therefore, it is impossible that (A) and (B) represent the number of cars produced outside of Michigan. Choices (A) and (B) can be eliminated. The only answer that remains is (C), which is the correct answer. Note that (C) is also close to our estimate of the answer.

Let’s look at that same problem again, but for a different reason:

Twenty-two percent of the cars produced in the United States are manufactured in Michigan. If the United States produces a total of 40 million cars, how many of these cars are produced outside of Michigan?

8.8 million

18 million

31.2 million

48.8 million

62 million

So, let’s now assume that you are running low on time for the Quantitative section of the test and you come across this question. You’re comfortable with percentages, so you decide that you can rush your way through this question. You quickly realize the first step in this problem is to find out how many actual cars are produced in Michigan; in other words, you need to know what 22 percent of 40 million equals. You do the calculation to determine that 8.8 million is 22% of 40 million. Your eye catches (A), which is an exact match for the number you just got, so you select (A) and move on to the next question.

The only problem is that you got the question wrong because you fell for a partial answer.

We discussed partial answers in Chapter 5 in some detail. Partial answers are answer choices that match a correct calculation for part of a question. The GMAT test-writers love to include partial answers. Partial answers are particularly tricky when you’re in a rush as they are designed to be appealing to test-takers who don’t read the full question, or who are in a hurry.

How can you use this information to your advantage? When you are looking to guess on a question, it helps to think critically about the answer choices. Does a certain answer choice look too obvious or easy? If so, there’s a good chance it’s a partial answer and, absent doing the actual problem, would be a good candidate to be eliminated before you guess.

Many times partial answers also come in the form of answers that can be derived from one step, or answers that contain numbers or variables that are similar to those found in the problem. If you’re pressed for time and looking to guess, look for these types of answer choices to eliminate.

Finally, the best way to avoid partial answers is to get into the habit of reading the question stem one more time before selecting your answer. That way, you can be sure that you are answering the question that was asked!

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Putting It All Together

Try the following problem and look for ways to eliminate answer choices using Ballparking and partial answers.

The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 20%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?

20%

24%

30%

32%

70%

Here’s How to Crack It

The factory raises its output by 10% and then raises it again by 20%. The problem is asking for the amount the factory will need to lower its output to return to the original level. For this example, don’t worry about solving the problem. Just practice eliminating incorrect answer choices using Ballparking or partial answers.

Choice (A) is just a repeat of the numbers in the question, which is a warning sign of a partial answer, so eliminate (A). Choice (C) is the result of adding the two percentages in the question together. This is too easy and a warning sign of a partial answer, so eliminate (C). Choice (E) is significantly greater than the information in the problem would suggest. Even if it’s unclear by how much the factory needs to lower its output, the amount by which the factory raised its output is not even close to 70%. Eliminate (E).

The remaining answer choices, (B) and (D), are not as easily eliminated as (A), (C), and (E). Figuring out which answer to eliminate next would require solving the problem. However, if you are in a rush or do not know how to answer this question, you could have eliminated three of the five answer choices and given yourself a 50/50 shot at correctly guessing the answer to the question. Those are better odds than guessing blindly! The correct answer, by the way, is (B).

20％

24％

30％

32％

70％

Look at another example:

A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 90 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?

79

89

95

95.5

97.2

Here’s How to Crack It

Again, assume you’re running out of time or are unsure how to solve this problem. Can you eliminate any answer choices to improve your odds of correctly guessing the answer? The problem states that the student received average grades of 100 and 90 in a two-year period. The question wants to know the average grade of the student for the entire two-year period. If the least grade the student averaged is 90, it is not possible for the student’s average to be less than 90, so (A) and (B) can be eliminated. Choice (C) has all the warning signs of a partial answer, as 95 is just the average of 100 and 90, the two numbers found in the problem, so (C) is also a good candidate to be eliminated.

The remaining answer choices are not as easy to eliminate. But again, by applying these POE strategies, you were able to give yourself a 50/50 shot at correctly guessing the answer! The correct answer here is (D).

79

89

95

95.5

97.2

Summary

Process of Elimination allows you to eliminate answer choices even when you don’t know how to do a problem or you are running out of time. There are two types of answer choices to look for in these situations: Ballparking and partial answers.

Ballparking: Some GMAT answer choices can easily be found to be false by using rough estimates of numbers in the problem that make the numbers easier to work with.

Partial answers: GMAC likes to include, among the answer choices, answers that are partial completions of the problem. Recognize these answer choices by looking for choices that require little or no work, or are similar to the numbers in the problem.

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