Data Sufficiency: Basic Principles

Data Sufficiency is a question type you’ve never seen before. This chapter will show you how to use basic POE techniques to make this format your new favorite kind of math.

 

Almost half of the 31 math questions on the GMAT will be Data Sufficiency questions. We’re about to show you how to use POE to make this strange question type easy.

 

WHAT IS DATA SUFFICIENCY?

If you’ve never heard of Data Sufficiency, that’s because this question type is unique to the GMAT, and these questions definitely require some getting used to. If you have already taken a GMAT practice exam, or the actual GMAT, you may have spent several minutes just trying to understand the directions for Data Sufficiency questions.

 

However, Data Sufficiency questions really just test the same math concepts as Problem Solving questions, but with a twist—a strange question format.

 

Here’s what a Data Sufficiency question looks like on the GMAT:

數據充分性:基本原則

數據充分性是您從未見過的問題類型。 本章將向您展示如何使用基本的POE技術使這種格式成為您最喜歡的一種數學形式。

 

GMAT上的31個數學問題中,幾乎有一半是數據充足性問題。 我們將向您展示如何使用POE簡化這種奇怪的問題類型。

 

什麼是數據充實度?

如果您從未聽說過數據充分性,那是因為此問題類型是GMAT特有的,並且這些問題肯定需要一定的習慣。 如果您已經參加了GMAT實踐考試或實際的GMAT,那麼您可能已經花了幾分鐘的時間試圖理解有關數據充足性問題的說明。

 

但是,數據充足性問題實際上只是測試了與“解決問題”問題相同的數學概念,但有一個曲折-一種奇怪的問題格式。

 

這是GMAT上的數據充足性問題的樣子:

What is the value of y ?

 

(1) y is an even integer such that –1.5 < y < 1.5

 

(2) Integer y is not prime

 

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

 

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

 

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

 

EACH statement ALONE is sufficient.

 

Statements (1) and (2) TOGETHER are not sufficient.

 

Each Data Sufficiency question consists of a question followed by two statements. There are also five possible answer choices, as shown. The answers are the same for every Data Sufficiency question, so once you learn what each means, you won’t need to spend time rereading them. You’ll just be able to think about them as answers (A), (B), (C), (D), and (E), which is how we’ll refer to them.

 

Notice that there are two words that the answer choices keep repeating—alone and sufficient. So, it looks like we’re supposed to evaluate the statements on their own—at least at first. Moreover, our task is evidently to determine whether we have sufficient information to answer the question.

 

That’s how Data Sufficiency differs from Problem Solving. In Problem Solving questions, you are asked to give a numerical answer to the question. In fact, the inclusion of five numerical answer choices tells you that you can assume that the question can be solved. For Data Sufficiency questions, however, you’re not being asked to solve the question but to decide WHETHER the question can be solved. It may, in fact, turn out that the statements do not provide sufficient information to answer the question.

y的值是多少?

 

(1)y是一個偶數,使得–1.5 <y <1.5

 

(2)整數y不是素數

 

陳述(1)僅是足夠的,但僅陳述(2)是不夠的。

 

陳述(2)單獨就足夠了,但是僅陳述(1)不夠。

 

兩條語句TOGETHER都足夠,但是NEITHER語句ALONE就足夠了。

 

每個語句ALONE就足夠了。

 

語句(1)和(2)不夠。

 

每個數據充足性問題均包含一個問題,後跟兩個陳述。如圖所示,還有五個可能的答案選擇。每個數據充足性問題的答案都是相同的,因此,一旦了解了每種含義,您就無需花時間重新閱讀它們。您只需將它們視為答案(A),(B),(C),(D)和(E),這就是我們對它們的稱呼。

 

請注意,答案選擇有兩個詞會不斷重複:一個詞就足夠。因此,看來我們應該至少自己評估一下這些陳述。此外,我們的任務顯然是確定我們是否有足夠的信息來回答問題。

 

這就是數據充足性與解決問題的不同之處。在“解決問題”中,要求您為問題提供數字答案。實際上,包含五個數字答案選項可以告訴您可以假定問題可以解決。但是,對於數據充足性問題,不是要求您解決問題,而是要決定是否可以解決問題。實際上,事實證明,這些陳述沒有提供足夠的信息來回答問題。

Here’s How to Crack It

 

The first answer choice—(A)—indicates that we should first look at Statement (1) by itself to see if it is sufficient to answer the question.

 

In fact, the best way to work Data Sufficiency problems is to look at one statement at a time. So, ignore Statement (2). Here, we’ve replaced Statement (2) with question marks to indicate that we are looking only at the first statement—almost as though we had covered up the second statement.

 

What is the value of y ?

 

(1) y is an even integer such that –1.5 < y < 1.5.

 

(2) ????

 

Now, we’re ready to evaluate Statement (1) alone. There are three integers between –1.5 and 1.5: –1, 0, and 1. Of those, as you may recall from Chapter 7, only 0 is even. So, Statement (1) does provide sufficient information to answer the question.

 

We’re not ready to choose the first answer—(A)—yet, however, because the second part of the answer choice states that Statement (2) alone is not sufficient. Now, forget that you have ever seen Statement (1).

 

What is the value of y ?

 

(1) ????

 

(2) Integer y is not prime.

 

The second statement tells us only that y is not prime. So, possible values for y include 1, 4, 6, 8, etc. Do we know the value of y? No way. So, Statement (2) is not sufficient. Because (1) is sufficient and (2) is not, the answer to this question is

 

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

 

Or, in other words, the correct answer is (A).

這是破解方法

 

第一個答案選擇(A)表示我們首先應單獨查看語句(1),以了解是否足以回答該問題。

 

實際上,解決數據充足性問題的最佳方法是一次查看一個語句。因此,忽略語句(2)。在這裡,我們用問號替換了語句(2),以表示我們僅查看第一個語句-就像掩蓋了第二個語句一樣。

 

y的值是多少?

 

(1)y是一個偶數整數,使得–1.5 <y <1.5。

 

(2)????

 

現在,我們準備單獨評估語句(1)。在–1.5和1.5之間有三個整數:–1、0和1。正如您可能在第7章中回憶的那樣,其中只有0是偶數。因此,聲明(1)確實提供了足夠的信息來回答問題。

 

但是,我們還沒有準備好選擇第一個答案(A),因為答案選擇的第二部分指出僅陳述(2)是不夠的。現在,忘記您曾經看過語句(1)。

 

y的值是多少?

 

(1)????

 

(2)整數y不是素數。

 

第二條語句僅告訴我們y不是素數。因此,y的可能值包括1、4、6、8等。我們知道y的值嗎?沒門。因此,陳述(2)是不夠的。因為(1)足夠而(2)不足夠,所以這個問題的答案是

 

陳述(1)僅是足夠的,但僅陳述(2)是不夠的。

 

或者,換句話說,正確答案是(A)。

DATA SUFFICIENCY: GETTING STARTED

Now that you’ve seen and worked a Data Sufficiency question, it’s time to learn how to make this weird question type your own. The first step is to understand what each of the answer choices means.

 

By making small changes to the example you’ve just seen, we can provide examples of each of the answer choices. Next to each example, you’ll find a graphic that provides a quick and dirty way to understand and remember each answer choice. Here’s the example for (A) again:

 

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

 

What is the value of y ?

 

(1) y is an even integer such that

 

–1.5 < y < 1.5.

 

數據充實性:入門

既然您已經看到並處理了數據充足性問題,那麼現在該學習如何將這種奇怪的問題鍵入您自己的類型了。 第一步是了解每種答案選擇的含義。

 

通過對您剛才看到的示例進行一些小的更改,我們可以提供每個答案選擇的示例。 在每個示例旁邊,您都可以找到一個圖形,該圖形提供了一種快速而骯髒的方式來理解和記住每個答案的選擇。 再次是(A)的示例:

 

陳述(1)僅是足夠的,但僅陳述(2)是不夠的。

 

y的值是多少?

 

(1)y是一個偶數,使得

 

–1.5 <y <1.5。

(2) Integer y is not prime.

 

Now, let’s make some changes to the statements, to get an example of (B).

 

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

 

What is the value of y ?

 

(1) Integer y is not prime.

 

(2)整數y不是質數。

 

現在,讓我們對語句進行一些更改,以得到(B)的示例。

 

陳述(2)單獨就足夠了,但是僅陳述(1)不夠。

 

y的值是多少?

 

(1)整數y不是質數。

(2) y is an even integer such that

 

–1.5 < y < 1.5.

 

As you can see from this example, (B) is pretty much the flip side of (A). In this case, the first statement provides no help in determining the value of y, but the second statement tells us that y = 0.

 

A few more changes produce an example of (C).

 

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

 

What is the value of y ?

 

(1) y is an even integer.

(2)y是一個偶數,使得

 

–1.5 <y <1.5。

 

從該示例可以看出,(B)幾乎是(A)的另一面。 在這種情況下,第一條語句對確定y的值沒有幫助,但是第二條語句告訴我們y = 0。

 

還有一些變化產生了(C)的示例。

 

兩條語句TOGETHER都足夠,但是NEITHER語句ALONE就足夠了。

 

y的值是多少?

 

(1)y是偶數整數。

 

Now that you’ve seen and worked a Data Sufficiency question, it’s time to learn how to make this weird question type your own. The first step is to understand what each of the answer choices means.

 

By making small changes to the example you’ve just seen, we can provide examples of each of the answer choices. Next to each example, you’ll find a graphic that provides a quick and dirty way to understand and remember each answer choice. Here’s the example for (A) again:

 

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

 

What is the value of y ?

 

(1) y is an even integer such that

 

–1.5 < y < 1.5.

 

 

(2) Integer y is not prime.

 

Now, let’s make some changes to the statements, to get an example of (B).

 

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

 

What is the value of y ?

 

(1) Integer y is not prime.

 

 

(2) y is an even integer such that

 

–1.5 < y < 1.5.

 

As you can see from this example, (B) is pretty much the flip side of (A). In this case, the first statement provides no help in determining the value of y, but the second statement tells us that y = 0.

 

A few more changes produce an example of (C).

 

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

 

What is the value of y ?

 

(1) y is an even integer.

 

 

(2) –1.5 < y < 1.5

 

The first statement tells us that y is even, but there are a lot of even integers. The second statement gives us a range of values for y, but, by itself, we don’t even know that y is an integer from the second statement. So, neither statement is sufficient on its own. But, when we put them together, we know that y = 0.

 

Now, let’s get an example of (D).

 

EACH statement ALONE is sufficient.

 

What is the value of y ?

 

(1) y is an even integer such that

 

–1.5 < y < 1.5.

 

既然您已經看到並處理了數據充足性問題,那麼現在該學習如何將這種奇怪的問題鍵入您自己的類型了。第一步是了解每種答案選擇的含義。

 

通過對您剛才看到的示例進行一些小的更改,我們可以提供每個答案選擇的示例。在每個示例旁邊,您都可以找到一個圖形,該圖形提供了一種快速而骯髒的方式來理解和記住每個答案的選擇。再次是(A)的示例:

 

陳述(1)僅是足夠的,但僅陳述(2)是不夠的。

 

y的值是多少?

 

(1)y是一個偶數,使得

 

–1.5 <y <1.5。

 

 

(2)整數y不是素數。

 

現在,讓我們對語句進行一些更改,以得到(B)的示例。

 

陳述(2)單獨就足夠了,但是僅陳述(1)不夠。

 

y的值是多少?

 

(1)整數y不是素數。

 

 

(2)y是一個偶數,使得

 

–1.5 <y <1.5。

 

從該示例可以看出,(B)幾乎是(A)的另一面。在這種情況下,第一條語句對確定y的值沒有幫助,但是第二條語句告訴我們y = 0。

 

還有一些變化產生了(C)的示例。

 

兩條語句TOGETHER都足夠,但是NEITHER語句ALONE就足夠了。

 

y的值是多少?

 

(1)y是偶數整數。

 

 

(2)–1.5 <y <1.5

 

第一個語句告訴我們y是偶數,但是有很多偶數整數。第二條語句為我們提供了y的值範圍,但就其本身而言,我們甚至都不知道y是第二條語句中的整數。因此,這兩個陳述本身都不足夠。但是,當我們將它們放在一起時,我們知道y = 0。

 

現在,讓我們舉一個(D)的例子。

 

每個語句ALONE就足夠了。

 

y的值是多少?

 

(1)y是一個偶數,使得

 

–1.5 <y <1.5。

(2) For any integer a ≠ 0, ay = 0.

 

As pointed out in previous examples, the information in Statement (1) allows us to conclude that y = 0. The information in the second statement also tells us that y is 0, because the only way for the product of ay to equal 0 is if either a or y is 0. Since a can’t be 0, y must be 0. Note how the statements independently allow us to arrive at the conclusion that y = 0 for (D).

 

Finally, let’s look at an example of (E).

 

Statements (1) and (2) TOGETHER are not sufficient.

 

What is the value of y ?

 

(1) y is an even integer.

(2)對於任何a≠0的整數,ay = 0。

 

如前面的示例所指出的,語句(1)中的信息使我們可以得出y = 0的結論。第二條語句中的信息還告訴我們y為0,因為ay等於0的乘積的唯一方法是 如果a或y為0。由於a不能為0,因此y必須為0。請注意,這些語句如何獨立地使我們得出(D)y = 0的結論。

 

最後,讓我們看一個(E)的例子。

 

語句(1)和(2)不夠。

 

y的值是多少?

 

(1)y是偶數整數。

(2) Integer y is not prime.

 

For this example, there’s no way to determine the value of y. The first statement doesn’t work because y could be any even integer. The second statement also doesn’t help because y can be any integer that isn’t prime. Even when we combine the statements, we don’t know the value of y because any even integer except 2 fits the conditions. So, (E) is the no way, no how answer.

 

Below, you’ll find the full graphic for all of the answers. You may find it helpful to keep the graphic handy until you are completely comfortable with what each answer choice means.

(2)整數y不是素數。

 

在此示例中,無法確定y的值。 第一條語句無效,因為y可以是任何偶數整數。 第二條語句也無濟於事,因為y可以是任何不是素數的整數。 即使我們合併這些語句,我們也不知道y的值,因為除2以外的任何偶數均符合條件。 因此,(E)是沒有辦法,沒有答案。

 

在下面,您將找到所有答案的完整圖形。 您可能會發現保持圖形方便有用,直到您完全滿意每種答案選擇的含義為止。

DATA SUFFICIENCY: BASIC POE STRATEGY

One of the reasons the test-writers decided to include Data Sufficiency questions on the GMAT is that when this format was first dreamed up they thought these questions would be immune to Process of Elimination (POE). Were they ever wrong! If anything, it’s even easier to apply POE to Data Sufficiency questions. Let’s see why.

 

First, however, let’s restate one of the most important strategies for working any Data Sufficiency question: Evaluate the statements one at a time before you think about combining them. Many people mistakenly pick (C)—you need both statements together—when it would have been possible to answer the question with only the information in the first statement or the second statement. Generally, people make this mistake when they read both statements right after reading the question stem. In fact, this mistake is the most common mistake that test-takers make when working Data Sufficiency questions.

 

To avoid this common mistake, read the question stem and only the first statement. Ignore the second statement. Pretend it isn’t there. You may even go as far as covering Statement (2) with your finger if you find the temptation to read both statements too overpowering. Once you have evaluated Statement (1), forget it. Ignore it. It doesn’t exist anymore. Cover it up if you need to and read and evaluate Statement (2).

 

What happens when you evaluate the statements one at a time? Something magical, that’s what! POE comes roaring back. Consider the following partial example:

 

What is the value of x ?

 

(1) x + 7 = 12

數據充分性:基本POE策略

測試編寫者決定在GMAT上包含數據充足性問題的原因之一是,當初次想到這種格式時,他們認為這些問題將不受淘汰過程(POE)的影響。他們曾經錯過!如果有的話,將POE應用於數據充足性問題甚至更容易。讓我們看看為什麼。

 

但是,首先,讓我們重申解決任何數據充足性問題的最重要策略之一:在考慮組合它們之前,一次評估一個語句。當許多人可能只用第一條或第二條陳述中的信息來回答問題時,就會錯誤地選擇(C)(您同時需要兩個陳述)。通常,人們在閱讀問題詞乾後立即閱讀兩個陳述時會犯此錯誤。實際上,此錯誤是考生處理數據充足性問題時最常見的錯誤。

 

為避免此常見錯誤,請閱讀問題詞乾和僅第一條陳述。忽略第二條語句。假裝它不在那裡。如果您發現閱讀這兩個陳述的誘惑力太大,您甚至可能會用手指覆蓋陳述(2)。評估完陳述(1)後,就算了。忽略它。它不存在了。如果需要,請掩蓋,並閱讀和評估聲明(2)。

 

一次評估一個語句會發生什麼?神奇的東西! POE咆哮回來。考慮下面的部分示例:

 

x的值是多少?

 

(1)x + 7 = 12

We don’t even have Statement (2), but we can still do a lot with this partial question. (Don’t worry. There won’t be any partial questions on the real test!) First, you want to see if the statement is sufficient to answer the question. In this case, you could subtract 7 from both sides of the equation to discover that x = 5. We’ll take this as an opportunity to remind you, however, that you don’t really need to solve the equation—you just need to know that you can solve the equation. After all, to pick an answer to the problem, you just need to know if you have sufficient information.

 

Since Statement (1) is sufficient in this case, which answer choices can be eliminated? From the chart, you can see that there are only two answer choices—(A) and (D)—that have Statement (1) circled to indicate that, for that answer choice, Statement (1) is sufficient. So, you no longer need to worry about (B), (C), or (E). They’ve been eliminated! If the first statement is sufficient, the answer to the problem must be (A) or (D)! You’re down to 50/50 just based on looking at the first statement!

我們甚至沒有陳述(2),但是對於這個部分問題我們仍然可以做很多事情。 (不用擔心。在實際測試中不會有任何部分問題!)首先,您想查看該陳述是否足以回答問題。在這種情況下,您可以從方程式的兩邊都減去7來發現x =5。我們藉此機會提醒您,但是,您實際上並不需要求解方程式,您只需要知道您可以求解方程式。畢竟,要選擇問題的答案,您只需要知道您是否有足夠的信息即可。

 

由於在這種情況下陳述(1)就足夠了,因此可以消除哪些答案選擇?從圖表中可以看到,只有兩個答案選項(A)和(D)帶有語句(1)圈出,表示對於該答案選擇,語句(1)就足夠了。因此,您不再需要擔心(B),(C)或(E)。他們被淘汰了!如果第一個陳述足夠,則問題的答案必須為(A)或(D)!僅查看第一條語句,您就降至50/50!

Now, check out this example:

 

What is the value of x ?

 

(1) x is an integer.

 

Now, what are the possible answers? If you said (B), (C), or (E), you are well on your way to getting this Data Sufficiency stuff under control. If you said something else, take a look at the steps outlined previously. In this case, the first statement is insufficient to determine the value of x. So, you want the answer choices that have 1 crossed off, and that is (B), (C), or (E).

現在,查看以下示例:

 

x的值是多少?

 

(1)x是整數。

 

現在,可能的答案是什麼? 如果您說的是(B),(C)或(E),那麼您就可以很好地控制此數據充足性。 如果您還有其他話,請看一下前面概述的步驟。 在這種情況下,第一個語句不足以確定x的值。 因此,您希望選擇的答案中有1個被劃掉,即(B),(C)或(E)。

DRILL 1: (AD/BCE)

In the following drill, each question is followed by only one statement. Based on the first statement, decide if you are down to AD or BCE. The answers can be found in Part VI.

 

1. What is the value of x ?

 

(1) y = 4

 

(2) ????

 

2. Is y an integer?

 

(1) 2y is an integer.

 

(2) ????

 

3. A certain room contains 12 children. How many more boys than girls are there?

 

(1) There are three girls in the room.

 

(2) ????

 

4. What number is x percent of 20 ?

 

(1) 10 percent of x is 5.

 

(2) ????

練習1:(AD / BCE)

在下面的練習中,每個問題後僅是一個陳述。 根據第一條陳述,確定您是AD還是BCE。 答案可以在第六部分中找到。

 

1. x的值是多少?

 

(1)y = 4

 

(2)????

 

2. y是整數嗎?

 

(1)2y是整數。

 

(2)????

 

3.某個房間可容納12個孩子。 男孩比女孩多多少?

 

(1)房間裡有三個女孩。

 

(2)????

 

4. 20的百分之x是多少?

 

(1)x的10%為5。

 

(2)????

From AD or BCE to the Answer

Every time you start a Data Sufficiency question, you should read the question and only the first statement. If the first statement is sufficient, your possible answers are (A) or (D). If the first statement is insufficient, your possible answers are (B), (C), or (E). So, you can always get rid of either two or three answer choices just by evaluating the first statement. The AD/BCE split is so important that you’ll want to write down AD or BCE on your noteboard as you work every Data Sufficiency question.

從AD或BCE到答案

每次您啟動數據充足性問題時,都應閱讀該問題,並且僅閱讀第一條陳述。 如果第一個陳述足夠,則可能的答案是(A)或(D)。 如果第一個陳述不夠充分,則可能的答案是(B),(C)或(E)。 因此,僅通過評估第一條陳述,您始終可以擺脫兩個或三個答案選擇。 AD / BCE拆分非常重要,因此您在處理每個數據充足性問題時都希望在記事板上寫下AD或BCE。

But what happens next? How do you get to the answer? Let’s take a look.

 

If x + y = 3, what is the value of xy ?

 

(1) x and y are integers.

 

(2) x and y are positive.

 

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

 

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

 

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

 

EACH statement ALONE is sufficient.

 

Statements (1) and (2) TOGETHER are not sufficient.

 

Here’s How to Crack It

 

As always, ignore Statement (2) and look only at Statement (1). If x and y are integers and x+y = 3, do we know what they are? Not really—x could be 1 and y could be 2 (in which case, xy would be 2). But x could also be 0 (yes, 0 is an integer) and y could be 3 (in which case, xy would be 0). Because Statement (1) alone is not sufficient, we are down to BCE, a one in three shot.

 

Now, ignore Statement (1) and look at Statement (2). By itself, this statement doesn’t begin to give us values for x and y—x could be 1 and y could be 2, but x could just as easily be 1.4 and y could be 1.6. Because there is still more than one possible value for xy, cross off (B).

 

We’re down to (C) or (E). Now it’s finally time to look at both statements at the same time. See how late in the process we combine the statements? Get into the habit of physically crossing off (B) before you think about combining the statements. That’s how you can avoid making the most common GMAT Data Sufficiency mistake of putting the statements together too early.

 

Because we know from the first statement that x and y are integers, and from the second statement that they must be positive, do we now know specific values for x and y?

 

Well, we do know that there are only two positive integers that add up to 3: 2 and 1. (Remember, zero is an integer but it is neither positive nor negative.)

 

Do we know if x = 1 and y = 2, or vice versa? Not really, but frankly, it doesn’t matter in this case. The question is asking us the value of xy.

 

Because neither statement by itself is sufficient, but both statements together are sufficient, the answer is (C).

但是接下來會發生什麼呢?您如何得到答案?讓我們來看看。

 

如果x + y = 3,則xy的值是多少?

 

(1)x和y是整數。

 

(2)x和y為正。

 

陳述(1)僅是足夠的,但僅陳述(2)是不夠的。

 

陳述(2)單獨就足夠了,但是僅陳述(1)不夠。

 

兩條語句TOGETHER都足夠,但是NEITHER語句ALONE就足夠了。

 

每個語句ALONE就足夠了。

 

語句(1)和(2)不夠。

 

這是破解方法

 

與往常一樣,忽略語句(2),僅查看語句(1)。如果x和y是整數且x + y = 3,我們知道它們是什麼嗎?並非完全正確,x可以為1,y可以為2(在這種情況下,xy為2)。但是x也可以是0(是,0是整數),y可以是3(在這種情況下,xy將是0)。因為僅陳述(1)不夠,所以我們要依靠BCE,三分之二。

 

現在,忽略語句(1),然後查看語句(2)。就其本身而言,該語句並沒有開始為我們提供x和y的值-x可以為1,y可以為2,但是x可以很容易地為1.4,y可以為1.6。因為xy仍然有多個可能值,所以將其捨去(B)。

 

我們只剩下(C)或(E)。現在終於可以同時查看兩個陳述了。看看我們在多長時間後合併這些語句?在考慮合併語句之前,養成在物理上偏離(B)的習慣。這樣一來,您就可以避免犯最常見的GMAT數據充裕性錯誤,即過早地將語句組合在一起。

 

因為我們從第一個語句中知道x和y是整數,並且從第二個語句中知道它們必須是正數,所以我們現在知道x和y的特定值嗎?

 

好吧,我們確實知道只有兩個正整數加起來等於3:2和1。(請記住,零是整數,但既不是正數也不是負數。)

 

我們是否知道x = 1和y = 2,反之亦然?並非如此,但坦白說,在這種情況下,這並不重要。問題是問我們xy的值。

 

因為這兩個陳述本身都不足夠,但是兩個陳述加在一起就足夠了,答案是(C)。

Here’s a handy flowchart that shows you what to do for any Data Sufficiency problem. You should keep the flowchart next to you and consult it as you first start practicing Data Sufficiency questions. After you have done 10 or 20 questions, you’ll probably find that you have learned the basic POE process well enough that you don’t need the chart anymore. However, if you ever find yourself having trouble with Data Sufficiency, pull out the chart again and do some more problems, using it as a guide.

這是一個方便的流程圖,向您顯示如何解決任何數據充足性問題。 您應該保留流程圖旁邊的內容,並在您第一次開始練習數據充足性問題時查閱該流程圖。 完成10或20個問題後,您可能會發現您已經充分了解了POE的基本流程,因此不再需要該圖表。 但是,如果您發現自己在數據充足性方面遇到麻煩,請再次將圖表拔出並做更多的問題,並以此為指導。

YES/NO DATA SUFFICIENCY: THE BASICS

If you were going to provide the answer to most Data Sufficiency questions, your response would be a number. However, as many as half of all the Data Sufficiency questions that you will see on your test will ask a yes-or-no question instead.

 

Leave it to GMAC to come up with a way to give you five different answer choices on a yes-or-no question. Let’s look at an example.

是/否  數據足夠:基礎

如果您要提供大多數數據充足性問題的答案,那麼您的回答將是數字。 但是,您將在測試中看到的所有數據充足性問題中,多達一半會詢問是或否問題。

 

將其留給GMAC提出,可以為您提供是或否問題的五個不同答案選擇。 讓我們看一個例子。

Did candidate x receive more than half of the 30,000 votes cast in the general election?

 

(1) Candidate y received 12,000 of the votes cast.

 

(2) Candidate x received 18,000 of the votes cast.

 

Here’s How to Crack It

 

When all is said and done, the answer to this question is either yes or no. Start by ignoring Statement (2) and evaluating Statement (1). Does Statement (1) alone answer the question? If you were in a hurry, you might think so. Many people assume that there are only two candidates in the election. They reason that if candidate y got 12,000 votes, then candidate x must have received 18,000 votes. However, there’s no reason to assume that there are only two candidates. So, Statement (1) is insufficient. Write down BCE. Does Statement (2) alone answer the question? Yes, it’s pretty clear that candidate x received more than half of the votes. So, the correct answer is (B).

候選人x是否獲得大選3萬張選票中的一半以上?

 

(1)候選人獲得12,000張選票。

 

(2)候選人x獲得18,000張選票。

 

這是破解方法

 

當一切都說完了,這個問題的答案是是或否。 首先忽略語句(2)並評估語句(1)。 陳述(1)單獨回答這個問題嗎? 如果您著急,您可能會這樣想。 許多人認為選舉中只有兩名候選人。 他們認為,如果候選人y獲得12,000票,那麼候選人x必須獲得18,000票。 但是,沒有理由假設只有兩個候選人。 因此,陳述(1)不足。 記下BCE。 陳述(2)單獨回答這個問題嗎? 是的,很明顯,候選人x獲得了一半以上的選票。 因此,正確答案是(B)。

That didn’t seem so bad, did it? Yet, you may have heard that yes/no Data Sufficiency questions have a reputation for being hard. Let’s change our example to see why.

好像還不錯,不是嗎? 但是,您可能已經聽說是/否數據充足性問題因很難而聞名。 讓我們更改示例以了解原因。

Did candidate x receive more than half of the 30,000 votes cast in the general election?

 

(1) Candidate y received 12,000 of the votes cast.

 

(2) Candidate x received 13,000 of the votes cast.

 

Here’s How to Crack It

 

As always, start by ignoring Statement (2) so that you can properly evaluate Statement (1) alone. As in our previous example, Statement (1) is insufficient, so be sure to write down BCE. Statement (2) seems pretty straightforward. Candidate x received fewer than half of the votes cast. At this point many people say, “Since the guy clearly got fewer than half the votes, this statement doesn’t answer the question, either.” But those people are wrong!

候選人x是否獲得大選3萬張選票中的一半以上?

 

(1)候選人獲得12,000張選票。

 

(2)候選人x獲得13,000張選票。

 

這是破解方法

 

與往常一樣,首先忽略語句(2),以便您可以單獨正確評估語句(1)。 與前面的示例一樣,語句(1)不足,因此請務必記下BCE。 陳述(2)似乎很簡單。 候選人x獲得的選票不到一半。 在這一點上,許多人說:“由於這個人明顯得不到一半的選票,所以這個陳述也沒有回答這個問題。” 但是那些人錯了!

Just Say No

Broken down to its basics, the question we were asked was, “Did he get more than half of the vote—yes or no?

 

Statement (2) does answer the question. The answer is, “No, he didn’t.” So, the answer is the same as that of the first example. The answer is (B).

勇敢說不

簡而言之,我們被問到的問題是:“他獲得了一半以上的選票嗎?是或否?

 

陳述(2)確實回答了這個問題。 答案是:“不,他沒有。” 因此,答案與第一個示例的答案相同。 答案是(B)。

On a yes/no Data Sufficiency problem, if the statement answers the question in either the affirmative or the negative, it is sufficient.

 

Yes/No/Maybe

Yes/no questions really should be called yes/no/maybe questions. Even if that’s not their “official” name, it’s still worthwhile to think about them in that fashion.

 

Let’s look at one last example to see why.

在是/否數據充足性問題上,如果語句以肯定或否定回答了問題,則足夠了。

 

是/否/也許

是/否問題實際上應該稱為是/否/也許是問題。 即使這不是他們的“正式”名稱,仍然值得以這種方式考慮他們。

 

讓我們看最後一個例子,了解原因。

Did candidate x receive more than half of the 30,000 votes cast in the general election?

 

(1) Candidate y received 12,000 of the votes cast.

 

(2) Candidate x received at least 13,000 of the votes cast.

 

Here’s How to Crack It

 

Since the first statement of this question is the same as that of the previous two examples, we know that it is insufficient. So, write down BCE. Now, let’s tackle Statement (2). Based on Statement (2), candidate x could have received exactly 13,000 votes, which would make the answer to the question “No, he did not receive more than half the votes cast.” However, he could have also received 16,000 votes, and that would make the answer to the question, “Yes, he did receive more than half the votes cast.” So, based on Statement (2), the best we can really say is that candidate x may have received more than half the votes. “Maybe” isn’t good enough—we need a definitive yes or no answer. So, Statement (2) is insufficient. Cross off (B). What if we combine the statements? We still have the same problem. We’ve accounted for at least 25,000 of the votes between the two candidates, but we don’t know about the other 5,000. All of those votes could have gone to candidate x, making the answer to the question “yes.” However, there could have been a third candidate who received those 5,000 votes. In that case, x would have received only 13,000 votes and the answer to the question is “no.” Combining the statements didn’t get us to a definitive answer. If the answer is sometimes “yes” and sometimes “no,” the statement is not sufficient. Cross off (C). The correct answer is (E).

候選人x是否獲得大選3萬張選票中的一半以上?

 

(1)候選人獲得12,000張選票。

 

(2)候選人x至少獲得13,000張選票。

 

這是破解方法

 

由於此問題的第一個陳述與前兩個示例相同,因此我們知道這是不夠的。因此,記下BCE。現在,讓我們解決語句(2)。根據聲明(2),候選人x可能恰好獲得13,000票,這將回答“不,他獲得的票數不超過一半”的問題。但是,他本來也可以得到16,000票,這將回答以下問題:“是的,他確實獲得了超過一半的選票。”因此,根據陳述(2),我們真正能說的最好的是,候選人x可能獲得了一半以上的選票。 “也許”還不夠好-我們需要確定的是或否答案。因此,陳述(2)不足。劃掉(B)。如果我們合併這些語句怎麼辦?我們仍然有同樣的問題。我們在兩位候選人之間至少贏得了25,000張選票,但我們對另外5,000張選票不知道。所有這些投票本可以投給候選人x,從而回答問題“是”。但是,可能會有第三位候選人獲得那5,000張選票。在這種情況下,x只會獲得13,000票,而問題的答案是“否”。合併這些陳述並不能使我們得到明確的答案。如果答案有時是“是”,有時是“否”,則該陳述是不夠的。劃掉(C)。正確答案是(E)。

MORE ON DATA SUFFICIENCY

Although Data Sufficiency problems test the same material covered by regular Problem Solving questions, some readers find it distracting to learn the more complicated subtleties of this new question type at the same time that they are learning (or relearning) math concepts. That’s why we’ve put our main chapter on Data Sufficiency at the end of our math review.

 

However, you will find Data Sufficiency problems sprinkled throughout the math drills—and you should feel free at any time to dip into Chapter 16, where you’ll find everything in one place, including more advanced strategy, several more drills, and some great techniques to handle the most complicated yes/no questions.

有關數據的更多信息

儘管數據充足性問題的測試內容與常規問題解決問題所涵蓋的內容相同,但是一些讀者發現,在學習(或重新學習)數學概念的同時學習這種新問題類型的更複雜的細微之處會分散注意力。 這就是為什麼我們在數學評論的最後放置了關於數據充分性的主要章節。

 

但是,您會發現遍歷整個數學練習的數據充足性問題–您隨時可以隨意進入第16章,在這裡可以找到所有內容,包括更高級的策略,更多的練習以及一些很棒的功能。 處理最複雜的是/否問題的技巧。

Summary

“Data Sufficiency” means just that, sufficiency. These questions are asking you if the data presented is enough to solve the problem.

 

Every Data Sufficiency problem consists of a question followed by two statements. You must decide whether the question can be answered based on the information in the two statements.

 

The best strategy for Data Sufficiency problems is to look at one statement at a time. Cover up the other statement with your hand, so that you can completely focus on one statement at a time.

 

AD or BCE: These are always your options when you first start eliminating. Memorize them.

概要

“數據充分性”就意味著充分性。 這些問題問您所提供的數據是否足以解決問題。

 

每個數據充足性問題均由一個問題後跟兩個語句組成。 您必鬚根據兩個語句中的信息來決定是否可以回答問題。

 

數據充足性問題的最佳策略是一次查看一個語句。 用手遮住另一條語句,以便您一次可以完全專注於一條語句。

 

AD或BCE:這些都是您首次開始淘汰時的選擇。 記住他們。

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