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.

緊急情況下打破玻璃

我們在本章中為您概述的策略經常被學生誤解。這並不是說概念太過困難或太過陌生。實際上，他們主要依靠簡單的邏輯推理，而只是密切關注問題。

但是，許多學生認為，這些策略是GMAT成功的一站式服務。顯然不是這樣。

當您遇到GMAT數學問題時，您的目標應該是使用本書涵蓋的數學概念和策略來解決該問題。每當屏幕上出現新的數學問題時，解決問題就應該是您的目標。您應該對問題進行內部清點（確定要測試的數學的種類，完成問題的可能步驟，問題提供的信息），然後進入數學工具包，以找到合適的工具來求解問題。

因此，這些POE策略不是解決數學問題的靈丹妙藥。他們不應該是您的首選。

這些策略應被視為應急閥。它們是最需要時拉動的拉力繩。這通常意味著您要嘛卡住了（解決方案無法解決問題），要嘛就沒時間了。

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.

難題

除非您是一位真正精通的數學家，否則由於某種原因，當天GMAT測試算法的自適應部分被破壞了（提示：不會發生），您最終將遇到一個數學問題，您將不知道該怎麼做。 解決。 你是做什麼？ 花很多時間來解決問題不一定是最好的主意，因為您還有其他需要解決的問題可能更容易解決。 因此，您決定猜測並繼續前進。 好主意！

可是等等！ 在您盲目猜測之前，請花一秒鐘並應用本章中概述的POE策略，以查看是否可以消除任何答案選擇。 您可能仍然需要猜測，但是如果您已經消除了一些答案選擇，則正確猜測的機率會更大。 這樣，您將有最大的機會正確回答其他難題，這將提高您的分數。

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!

時間不多了

假設您已經接近“定量”部分的分配時間，而您抬頭只是想知道您還有更多的問題要解決。 您知道為考試中的所有問題單擊答案是您的最大利益，因此您決定猜測其餘的問題。

可是等等！ 不要盲目猜測。 對於剩餘的問題，嘗試一些POE策略。 如果您能在猜測之前消除一些答案，那就太好了！

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

讓我們開始工作

既然我們已經確定了何時應該使用這些POE策略，那麼現在該討論實際策略了。 在本章的其餘部分中，我們將假定您已經嘗試使用數學概念來回答問題，而您沒有成功。 或者，您的時間不多了，需要對答案做出快速，有根據的猜測。 您已準備好砸碎玻璃並使用應急工具。 但是這些工具是什麼？您如何運用它們？

看一下下面的問題。 使用從第4章和第5章中學到的知識，是否可以使用POE消除任何答案選擇？

美國生產的汽車中有22％在密歇根州生產。 如果美國總共生產4000萬輛汽車，那麼其中有多少汽車在密歇根州以外生產？

880萬

1800萬

3120萬

4880萬

6200萬

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.

While Ballparking won’t usually get you to a single answer, it can often help you to eliminate some answers.

大致準確的

讓我們看看我們是否可以在不做任何繁重工作的情況下快速消除此問題的答案。問題是要問美國在密歇根州以外生產的4000萬輛汽車的數量。該問題還指出，美國生產的汽車中有22％在密歇根州生產，因此您知道美國生產的汽車中有78％是在密歇根州以外生產的。即使您不熟悉百分比，使用此信息也可以輕鬆消除任何答案選擇嗎？好吧，如果整個美國僅生產4000萬輛汽車，密歇根州以外的任何州都可能生產超過4000萬輛汽車嗎？不，不是，因此（D）和（E）可以消除，因為它們大於汽車總數。

此策略稱為“停球”。概括通常涉及對數字進行粗略比較或對答案大小進行粗略估計。在這種情況下，將答案選擇與問題中指出的生產的汽車總數進行比較，可以消除兩個答案選擇。

使用Ballparking還能消除其他答案嗎？讓我們嘗試大致估算答案的大小。如果在美國生產的汽車中有78％是在密歇根州以外生產的，那麼您知道在美國生產的4000萬輛汽車中，有超過四分之三是在密歇根州以外生產的。 4000萬的四分之三是3000萬。答案中的兩個（A）和（B）不到美國生產汽車總數的一半。因此，（A）和（B）代表密歇根州以外生產的汽車數量是不可能的。選項（A）和（B）可以消除。剩下的唯一答案是（C），這是正確的答案。請注意，（C）也接近我們對答案的估計。

雖然Ballparking通常不會讓您得到一個答案，但是它通常可以幫助您消除一些答案。

Partial Answers

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!

部分答案

讓我們再次看同樣的問題，但原因有所不同：

美國生產的汽車中有22％在密歇根州生產。如果美國總共生產4000萬輛汽車，那麼其中有多少汽車在密歇根州以外生產？

880萬

1800萬

3120萬

4880萬

6200萬

因此，現在假設您在測試“定量”部分的時間不夠用，並且遇到了這個問題。您對百分比很滿意，因此可以決定著急解決這個問題。您很快意識到這個問題的第一步是查明密歇根州實際生產了多少輛汽車。換句話說，您需要知道4000萬的22％是什麼。您進行計算以確定880萬是4000萬的22％。您的視線（A）與您剛得到的數字完全匹配，因此選擇（A）並轉到下一個問題。

唯一的問題是您錯了一個問題，因為您只得到了部分答案。

我們在第5章中詳細討論了部分答案。部分答案是與部分問題的正確計算相匹配的答案選擇。 GMAT測試編寫者喜歡包含部分答案。當您急忙時，部分答案特別棘手，因為它們的設計目的是吸引那些沒有閱讀完整問題或匆忙的應試者。

您如何利用這些信息來發揮自己的優勢？當您尋找問題的答案時，認真思考答案的選擇將很有幫助。某個答案選擇看起來是否太明顯或容易？如果是這樣，那麼很有可能是部分答案，而且如果不解決實際問題，將是一個很好的候選人，在您猜測之前就將其消除。

很多時候，部分答案也可以是從一個步驟中得出的答案，或者是包含與問題中發現的數字或變量相似的數字或變量的答案。如果您時間緊迫又想猜測，請尋找消除這些類型的答案。

最後，避免部分答案的最好方法是養成在選擇答案之前再閱讀一次問題的習慣。這樣，您可以確定自己在回答所提出的問題！

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).

放在一起

嘗試以下問題，並尋找使用Ballparking和部分答案來消除答案選擇的方法。

工廠的產量增加了10％，以適應不斷增長的需求。為了應對假期的高峰，這個新的產出增加了20％。為了恢復原始產量，現在必須將工廠的產量降低大約百分之幾？

20％

24％

30％

32％

70％

這是破解方法

工廠將其產量提高10％，然後再次提高20％。問題是要求工廠降低產量以恢復原始水平所需的數量。在此示例中，不必擔心解決問題。只需練習使用Ballparking或部分答案來消除錯誤的答案選擇。

選擇（A）只是問題中數字的重複，這是部分答案的警告信號，因此請消除（A）。選擇（C）是將問題中的兩個百分比加在一起的結果。這太容易了，並且會給出部分回答的警告信號，因此請消除（C）。選擇（E）遠大於問題中所提示的信息。即使不清楚工廠需要降低多少產量，工廠提高產量的金額甚至接近70％。消除（E）。

剩下的答案選擇（B）和（D）不像（A），（C）和（E）那樣容易消除。找出下一步要消除的答案將需要解決問題。但是，如果您急於或不知道如何回答該問題，則可以消除五個答案中的三個，並給自己50/50的射擊機會，以正確猜出問題的答案。這些比盲目猜測更好的賠率！正確的答案是（B）。

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).

再看一個例子：

去年，一名學生參加了6門課程，並獲得了100分的平均（算術平均值）分數。前一年，該學生參加了5門課程，平均成績為90分。到最近的十分之一點，學生在整個兩年中的平均成績是多少？

79

89

95

95.5

97.2

這是破解方法

同樣，假設您的時間用完了或不確定如何解決此問題。您能否消除任何答案選擇以提高正確猜出答案的機率？問題指出，該學生在兩年中的平均成績為100和90。問題想知道整個兩年期間學生的平均成績。如果學生的平均最低分數是90，則學生的平均分數不可能低於90，因此可以消除（A）和（B）。選擇（C）具有部分回答的所有警告信號，因為95只是平均值100和90（這是在問題中找到的兩個數字的平均值），因此（C）也是一個很好的被淘汰的選擇。

剩下的答案選擇不是那麼容易消除。但是同樣，通過應用這些POE策略，您可以正確地猜出答案，自己得到了50/50的機會！正確的答案是（D）。

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.

概要

消除過程使您可以消除答案選擇，即使您不知道如何解決問題或時間用盡。 在這些情況下，有兩種類型的答案可供選擇：推銷和部分答案。

推論：通過對問題中的數字進行粗略估算，可以很容易地發現一些GMAT答案選擇是錯誤的，從而使數字更易於使用。

部分答案：GMAC喜歡在答案選擇中包括部分問題的答案。 通過尋找需要很少或不需要工作或與問題中的數字相似的選擇來識別這些答案。