Negation Test Series: Article #1 - Understand Negation & Sample Spaces

Question

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Introduction A lot of students are scared of Assumption questions in the Critical Reasoning Section of the GMAT , simply because they are never really sure of the answer they are marking. The reason they face this problem is that they do not know how to exploit a key feature of any assumption . Needless to say that this lack in their understanding can cost them gravely since Assumption, together with related questions categories (such as Evaluate, Strengthen, Weaken etc.), accounts for more than 70% of the CR questions served in the exam . Before we go any further, why don’t you try an Official Assumption argument to have a firsthand experience of this question category: Argument: Although parapsychology is often considered a pseudoscience, it is in fact a genuine scientific enterprise, for it uses scientific methods such as controlled experiments and statistical tests of clearly stated hypotheses to examine the questions it raises. The conclusion above is properly drawn if which of the following is assumed? (A) If a field of study can conclusively answer the questions it raises, then it is a genuine science. (B) Since parapsychology uses scientific methods, it will produce credible results. (C) Any enterprise that does not use controlled experiments and statistical tests is not genuine science. (D) Any field of study that employs scientific methods is a genuine scientific enterprise. (E) Since parapsychology raises clearly statable questions, they can be tested in controlled experiments. What was your experience of the above question? Were you too unsure while marking the answer since you were confused between two answer choices? Did you have to re-read the passage while evaluating the answer choices, even though you did spend appropriate amount of time understanding the argument? If yes, then that means that you too are missing out on leveraging the Negation Test that exploits a central feature of an assumption - that it has to be true for the argument to hold true! To make you understand and master the concept of Negation test, we have designed this e-book. Through a step-by-step approach, we shall demonstrate how the Negation test can help you mark the correct answer to an assumption within less than 2 minutes and that too with a 100% surety. Accordingly, this e-book is divided into the following parts: https://gmatclub.com/blog/wp-content/uploads/2015/05/e-book-division-e1432703770569.png Alright, so let’s get started! Article #1: What is Negation and What are various Sample Spaces? Introduction The first step in understanding the Negation Test is to understand what negation means in the GMAT world. This is what we’ll cover first in this article. We’ll then understand how certain words play an important role in determining the scope of the sample space covered by the statement. Polar Opposite vs Logical Opposite Negation in the GMAT world is based on the concept of Logical Opposites . To understand what it means, let’s contrast it with Polar Opposite. https://gmatclub.com/blog/wp-content/uploads/2015/05/Polar-e1432704594917.png https://gmatclub.com/blog/wp-content/uploads/2015/05/Blank2-e1432709819561.png Polar Opposite : The polar opposite of a given word/phrase/statement is the extreme opposite of it; for instance cold is the polar opposite of hot. https://gmatclub.com/blog/wp-content/uploads/2015/05/Logical-e1432704466555.png Logical Opposite : The logical opposite range of a word/phrase/statement covers the spectrum of the possibilities that lie outside the arena of the negated word; for instance the logical opposite range that we get by negating the word “hot” would include possibilities such as moderately warm, lukewarm, cold etc. In all, this range includes anything and everything that is NOT hot. Hence, the logical opposite of “hot” is “not hot”. Below is a table that gives a few more examples to illustrate the difference between polar and logical opposites of a word. https://gmatclub.com/blog/wp-content/uploads/2015/05/table1-e1432704961531.png What is Negation in CR? Now that you have understood the concept of Logical Opposite, let’s see how we use the same to negate statements in CR. Let us take a couple of examples: Statement : The soup is hot. Negation : The soup is NOT hot. Meaning of the negated statement : We don’t know whether the soup is cold, moderately warm or lukewarm. All that we know is that it is definitely not hot . Statement : Michael plays basketball. Negation : Michael does NOT play basketball. Meaning of the negated statement : We don’t know whether Michael plays any other game. All that we know is that he definitely doesn’t play basketball . Easy, isn’t it? Let’s now look at another example. Statement : Isabelle’s hair is black. What will be the negation of the above statement? a. Isabelle’s hair is white. b. Isabelle’s hair is not black. Observe that (a) is the polar opposite of the given statement. With (a), you miss out on a lot of other possibilities; for instance, her hair could be neither black nor white - it could be red or brown. These possibilities are accounted for in the Logical Opposite of the statement, which in this case is: Isabelle’s hair is not black. (It is not necessary to specify the actual color.

) Meaning of the negated statement : We don’t know whether Isabelle’s hair is white or red or brown or some other color. All that we know for sure is that Isabelle’s hair is NOT black . In each of the given examples, we’re talking about only one person. So it is very easy for us to write down the negated statement. Let’s now increase the difficulty level a bit. Consider the following statement. Statement : All tall boys have black hair. Which of the following statements is/are the correct negation(s) for the above statement? a. Some tall boys have black hair. b. Not all tall boys have black hair. c. None of the tall boys have black hair. d. No boy has black hair. e. Most of the tall boys have black hair. Only choice (b) is the correct negation of the given statement. To understand why that is the case, we need to understand the concept of Sample Spaces . Let’s move to the same.

Understanding Sample Spaces The next step in understanding the concept of negation in Critical Reasoning is to understand exactly who/what the statement is talking about, i.e. the segment the statement talks about, and how this segment is affected by the sample space covered by the statement. This sample space is usually defined by various group markers such as: all, most, some, none etc. Let’s take a deeper look at these two aspects: Understanding the Segment : In the above example, the statement talks about a particular segment of population – All tall boys have black hair . So we need to consider the possibilities pertinent only to tall boys. We are not concerned with all boys, a group that includes short boys as well, or girls. ONLY tall boys are within the scope of the statement . This is the segment the statement talks about. Other segments are outside the scope of the argument and hence statements related to them are most likely not the correct assumptions. Understanding the Sample Space : Once you understand the segment being talked about, understand the sample space covered by the statement. Group-markers such as all, none, some, most, etc. define this sample space for the statement. Let’s say there are 100 tall boys (100 being a placeholder for “All” the elements in the segment). With this supposition, here is the sample space each group-marker covers: https://gmatclub.com/blog/wp-content/uploads/2015/05/table2.png It is helpful to think of these sample spaces in terms of the possibilities they represent. These possibilities can be represented on a straight line that denotes all the possibilities in the identified segment - we call this line the Possibility Line . Now, in the current example, we are concerned with the segment of tall boys. This segment consists of 100 tall boys. Since the Possibility Line will denote each and every possibility in this segment, we can diagrammatically represent the above group markers on it in the following ways: Diagram#1 shows the possibilities related to group markers none , some , not all , half , and all . https://gmatclub.com/blog/wp-content/uploads/2015/05/Possibility-Line-1-e1432707133170.png Diagram#2 shows the possibilities related to group markers none , less than half , up to half , half , most , and all . https://gmatclub.com/blog/wp-content/uploads/2015/05/Possibility-Line-2-e1432707558775.png Note : For the sake of clear understanding, the above group markers have been represented on two different Possibility Lines - you can represent them on a single Possibility Line as well. As you can see in the above diagrams, the statement All tall boys have black hair covers only one possibility point - not 99, not 98, not 14, but a point denoting the possibility that all 100 of them have black hair. Therefore, its logical negation should account for anything and everything that is NOT 100/ALL (0-99 tall boys). We will explore the concept of negating a statement in more detail in the next article, but before we move on to that, try your hand at solving the exercise questions given below. Practice Problems Try your hand at solving the problems given in the below link.

https://gmatclub.com/forum/questions-th ... 98825.html Good Luck!

P.S.: The pdf of this article is attached below.

egmat · Accepted Answer

Article #3: What is Negation Test and How to use it?

Introduction     
This is the third and the final article in the series of  Negation Test Articles . In the first article you learnt about the concept of logical negation and sample spaces. You also learnt how to represent various sample spaces on the Possibility Line. In the second article you applied this understanding to negate various statements. In this article, we’ll go one-step further and logically negate option choice statements through the  Negation Test to figure out the correct answer to an Assumption Question with a 100% surety .

All set to master the Negation Test? Let’s get rolling!

What is Negation Test?     
The Negation Test is a tool that we use to determine with full confidence as to whether a given answer choice in an Assumption question is the correct answer. How do we do that? We simply  take an answer choice and logically negate the information given in it . If by negating the information,  the conclusion is falsified , the answer choice at hand is indeed an assumption made by the author, and is, hence, the  correct answer . You can mark it and move on to the next question. As simple as that!

Of course  if negating  the information given in the answer choice under consideration  does not falsify the conclusion , you need to evaluate other contenders, since this one’s NOT the correct answer – it is  not the assumption ; it is not vital for the argument.

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt1-e1434271427788.png

Why does Negation Test work?    
Now you may ask as to why is that the case – why does negating the assumption falsify the conclusion?

The Negation Test exploits a key feature of any assumption – that the assumption has to be true for the conclusion to hold valid. Let’s understand this quality a bit more.

By definition, an  assumption is a   vital   piece of information  that is never actually given to us in the argument but is supposed/ assumed by the author while drawing the conclusion . What does this mean? This means that if  we take away the assumed piece of information , the author will not be able to draw the given conclusion and  the argument falls apart . This is the feature that the Negation Test utilizes.

Now that you know in principle why the Negation test works, let’s see it in action. But before that, you need to understand when exactly to use the test.

When to use Negation Test?    
To use the Negation test successfully, you need to understand when exactly to use it. The reasons for the same are simple:

1.  Negation Test is not meant as a first line of defence : The purpose of the test is to help you figure out the correct answer when you are stuck between two answer choices (ideally) that are close as per your understanding. This means that you will have done some analysis before using the test – we will show you what kind of analysis we mean.

2.  Using the test on each and every choice means wastage of precious prep/exam time : The test is meant to clear your doubt and help you save time while making a decision between answer choices that you think are close; however, if you apply it to each and every choice, then you are not only wasting your time but also missing a key gap in your understanding. The fact that you are confused among more than two answer choices shows that you didn’t understand the argument well. Applying the Negation Test will not work here since your understanding of the argument is not clear to begin with.

Now that you are clear about when to apply the Negation Test,  let’s address the analysis you should do leading up to its application .

Let’s say after you read an argument, you spend a little time on thinking about the argument, but, despite your best effort, the assumption doesn’t jump right at you. You, therefore, get confused when you go in to the answer-choice evaluation.

Now here’s how you should approach the question from this point on:

1.  Discard all the answer choices that do not provide new information : As discussed earlier, an assumption is something that is supposed/assumed but not stated by the author while making the conclusion. Therefore,  it cannot be a repetition of what’s already given to us .

2.  Discard answer choices that do not support the conclusion : As e-GMATers know, an assumption must always support the conclusion. The logic is the same.  Assumption provides a piece of information that the author has taken in to account while drawing the conclusion  – even though he/she doesn’t state it in the passage. So, basically, the  assumption facilitates the author in drawing the conclusion .

3.  Apply the Negation Test : After following the above two steps, you will be left with 2 (maybe 3 in the beginning when you are stilling learning concepts) answer choices. Now, without wasting any more time, get the Negation Test rolling.

Let’s see the above process in action.

Negation Test in Action: Example 1

Question    
 Argument : Investments that are not subject to market risk are categorised as conservative investment options. These options are generally safe to invest in but generate a lower than average market-yield. Therefore, some people over 60 are likely to get returns that are lower than the market average.

Which of the following is an assumption made by the author?

A. Most people over 60 are likely to invest in conservative investment options.
B. At least one person over 60 is likely to invest in conservative investment options.
C. Some investors over 60 are likely to invest in options other than the ones generally considered conservative.

Before we apply the Negation Test to the three choices under consideration, let’s first understand the argument.

Passage Analysis    
The argument first tells us about a kind of investment option - conservative investment option. These investments have two features – safe to invest but yield lower than the market average. On the basis of this information, the author draws a conclusion about “some people over 60”. The author says that these people are likely to get return that are lower than the market average.

Initial Answer Choice Evaluation    
Now, let’s say you rejected a few answer choices on some basis or the other – they did not give any new information or they did not support the conclusion, and so they were irrelevant. For instance, in the given argument, Choice C is irrelevant. Now before we tell you why that’s the case, think for yourself. Does it talk about the relevant segment? NO. Does it give any information that increases our belief in the conclusion? NO- because it talks about the relevant group’s likelihood to invest in options other than the one the author concludes about.

So, here we are now:

Argument : Investments that are not subject to market risk are categorised as conservative investment options. These options are generally safe to invest in but generate a lower than average market-yield. Therefore, some people over 60 are likely to get returns that are lower than the market average.

Which of the following is an assumption made by the author?

A. Most people over 60 are likely to invest in conservative investment options. 
   Seems like a contender as it increases my faith in the conclusion - we now know that most people make such investments so their chances of getting lower than market average returns increase.

B. At least one person over 60 is likely to invest in conservative investment options. 
   Seems like a contender as it talks about the same segment making the mentioned investments but isn’t information about “most” above better than “at least” one here?

C.  Some investors over 60 are likely to invest in options other than the ones generally considered conservative. 
   Rejected for reasons mentioned above

Now is the time you should apply the Negation Test to choices A and B and see what impact the respective negated statements have on the conclusion. Let’s start with choice A.

Choice A    
 Choice A : Most people over 60 are likely to invest in conservative investment options.

Understand the Sample Space : We know that choice A talks about the relevant segment, so we can move to the step where we understand the sample space covered by choice A. Since it talks about “most” people over 60, the sample space it covers is:

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt2-e1434276537874.png

Now that we know the sample space it covers, we are ready to move to determining the possibilities that lie outside this sample space.

Understand the possibilities that lie outside the sample-space : Let’s see what possibilities lie outside the sample space covered by the group-marker  most .

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt3-e1434276606267.png

*Negated space = possibilities not covered by the original sample space

So, the negated statement we arrive at is:

Negated statement for choice A :   Up to 50%  of people over 60 are likely to invest in conservative investment options .

Impact of the negated statement on the Conclusion of the argument : The negated statement offers a range of possibilities. We’ll consider the extreme two ones for a clear understanding. They are:

1.   No  people over 60 are likely to invest in conservative investment options. –  falsifies the conclusion as it negates the possibility that people over 60 are likely to invest in such options.

2.   50%  of people over 60 are likely to invest in conservative investment options. –  strengthens the conclusion, as it indicates that half of the people in the segment are likely to invest in such options.

Now,  since the negated version of answer choice A does not falsify the conclusion in all possibilities under it, choice A is NOT the correct answer; it is not assumption made by the author.

By default, we are left with only one choice now - Choice B. But let’s apply the Negation Test and be a 100% sure that it is indeed the correct answer.

Choice B    
 Choice B : At least one person over 60 is likely to invest in conservative investment options.

Understand the Sample Space : Choice B says that at least one person in the segment is likely to invest in the mentioned investment options. Now, we know that logically speaking, “at least one” has the same meaning as “some” – we covered this derivation in the second article  How to Negate Statements  (read above). So, we can rephrase Choice B as:  Some people over 60 are likely to invest in conservative investment options.  Let’s represent the same on the Possibility Line:

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt4-e1434276662648.png

Understand the possibilities OUTSIDE the sample space : As you can see in the above section, the sample space covered by  some  is 1-100. Therefore, we are left with only one possibility on the Possibility Line that is OUTSIDE this space – the possibility of  none/no  or 0 people in the concerned segment. This is indeed the negated space. Let’s see it on the Possibility Line:

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt5-e1434276722285.png

Let’s now deduce the negated statement of Choice B by replacing the original group-marker by the negated space:

Choice B :   At least  one person over 60 is likely to invest in conservative investment options.

Negated version of Choice B :   None  of the people over 60 are likely to invest in conservative investment options.

Impact of the negated statement on the Conclusion of the argument : Is the conclusion falsified with the negated statement above? The answer to this question is a firm YES! The  negated statement  says that no one over 60 is likely to invest in such options. If that is indeed the case, then can the author draw the conclusion that “some” people over 60 are likely to get lower than average market-yield? Certainly not! The basis of the author’s conclusion is negated.

Since the negated version of answer choice B falsifies the conclusion distinctly- without any ambiguity - answer choice B is the CORRECT answer; it is indeed an assumption made by the author. 
 
 Note that in the examples we are going in to diagrammatic representations time and again. It is to illustrate what impact logical negation has on different statements. In the actual exam, you most likely won’t need to do so, as, with the right practice, you will have mastered logical negation in CR. Just in case you face a confusion then, you can use the Possibility Line to clear your doubt.

Now that you have seen how the Negation Test works in simple arguments, let’s apply it to an Official Question, which we have modified slightly.

Negation Test in Action: Example 2 (Official Question - Modified)     
 Argument :  Although parapsychology is often considered a pseudoscience, it is in fact a genuine scientific enterprise, for it uses scientific methods such as controlled experiments and statistical tests of clearly stated hypotheses to examine the questions it raises.

Remember the above argument? You must have tried it while reading the first article in the Negation Test series:  What is Negation and What are Various Sample Spaces  (read above). In the modified version, we have limited the answer choices to three, retained some of the original answer choices, and added some more from our end – this modification has been done to address some key gaps observed in students’ understanding of this question. Have a fresh look at the question:

Question    
 Argument : Although parapsychology is often considered a pseudoscience, it is in fact a genuine scientific enterprise, for it uses scientific methods such as controlled experiments and statistical tests of clearly stated hypotheses to examine the questions it raises.

The conclusion above is properly drawn if which of the following is assumed?

A. Every genuine scientific enterprise has to use scientific methods to examine the questions it raises.
B. Any field of study that employs scientific methods is a genuine scientific enterprise.
C. There is no other parameter, besides the use of scientific methods, that can singlehandedly determine whether a field is a genuine scientific enterprise.

Let’s see how the Negation Test helps us mark the right answer in this question, with full confidence. But before we do that, we must come to a common understanding of the argument. Accordingly, let’s analyse what the argument is all about.

Passage Analysis

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt6_new-e1434444727189.png

As you see,  the author’s conclusion rests on the fact that parapsychology uses scientific methods to examine the questions it raises . With this understanding in mind, let’s evaluate the answer choices:

Initial Answer Choice Evaluation

Argument : Although parapsychology is often considered a pseudoscience, it is in fact a genuine scientific enterprise, for it uses scientific methods such as controlled experiments and statistical tests of clearly stated hypotheses to examine the questions it raises.

A. Every genuine scientific enterprise has to use scientific methods to examine the questions it raises.
  Hmmm…I am not fully sure what this means…but let me keep it for now.

B. Any field of study that employs scientific methods is a genuine scientific enterprise.
   OK…this one makes the most sense, but I can’t reject the others with confidence.

C. There is no other parameter, besides the use of scientific methods, that can single-handedly determine whether a field is a genuine scientific enterprise.
  Seems like a contender as it definitely increases my faith in the conclusion - we now know that no other factor can on its own determine whether a field is a genuine scientific enterprise. I am going to keep it.

Now you can apply the Negation Test. Let’s negate each of the above statements to see what impact the negated versions have on the conclusion of the argument.

*Please note that we are going to put all the three answer choices under the Negation test since the purpose here is to show you how the test helps you evaluate answer choices that you might deem close. You should ideally use the test when you are stuck between two answer choices.

Choice A    
 Choice A :  Every genuine scientific enterprise has to use scientific methods to examine the questions it raises.

First of all, this choice is not a real contender for the Negation Test. Why is that the case? This choice talks about a must condition that all genuine scientific enterprises have to fulfil. But, if you consider the argument closely, you will see that  the argument does not conclude anything about all genuine scientific enterprises . The conclusion is regarding what can be considered as a good enough criterion for a field to be considered a genuine scientific enterprise.

Nevertheless, we will apply the Negation Test to this choice as, in our experience, many students get confused in such choices and end up marking them due to lack of proper understanding. With the application of the test, you will be able to see a 100% why it is incorrect.

Choice A :   Every  genuine scientific enterprise has to use scientific methods to examine the questions it raises.

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt7-e1434276863145.png

Negated version of Choice A :   Not every  genuine scientific enterprise has to use scientific methods to examine the questions it raises.

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt8-e1434276896773.png

Rephrase of the negated statement :   0 - 99  genuine scientific enterprises have to use scientific methods to examine the questions they raise.

Impact of the negated statement on the conclusion : The negated statement offers a range of possibilities. We’ll consider the two extreme ones for a clear understanding. They are:

1.   No  genuine scientific enterprises has to use scientific methods to examine the questions it raises. –    weakens the conclusion as it indicates that it is probably not a criterion worth considering.

2.   Almost all  genuine scientific enterprises have to use scientific methods to examine the questions they raise. –  strengthens the conclusion, as it indicates that it is a criterion worth considering.

As you can see, the negated version of choice A does not have a clear impact on the conclusion of the argument - it does not shatter the conclusion. Hence, choice A is not an assumption made by the author.

Choice B    
 Choice B :   Any  field of study that employs scientific methods is a genuine scientific enterprise.

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt9-e1434276942881.png

Negated version of Choice B :   Not all  fields of study that employ scientific methods are genuine scientific enterprises.

https://gmatclub.com/blog/wp-content/uploads/2015/06/NArt10-e1434276984266.png

Rephrase of the negated statement :   0-99  fields of study that employ scientific methods are genuine scientific enterprises.

Meaning of the negated statement : If you see, the above statement says that out of a 100 that employ scientific methods, only 0-99 are genuine scientific enterprises.  This means that there is definitely one possibility that a field employs scientific methods but is still not a genuine scientific enterprise.

Impact on the conclusion : The negated version of Choice B completely destroys the basis of the author’s conclusion. The reason the author said that parapsychology is a genuine scientific enterprise was that it uses scientific methods to examine the question it raises, implying that this factor is sufficient. However,  the negated version says that it is not sufficient as there is definitely 1 possibility in which even a field that uses scientific methods is not a genuine scientific enterprise. Hence, the conclusion is falsified. It is indeed the correct answer!

Even though we have arrived at the correct answer, we will see how the Negation Test helps us reject Choice C that we did consider as a contender in the beginning.

Choice C    
 Choice C :  There is  no  other parameter, besides the use of scientific methods, that can singlehandedly determine whether a field is a genuine scientific enterprise.

Negated version of Choice C :  There are  some  other parameters, besides the use of scientific methods, that can singlehandedly determine whether a field is a genuine scientific enterprise.

Meaning of the negated statement :  While the use of scientific methods can determine singlehandedly, there are some other methods as well.

Impact on the conclusion : Does this choice have any negative impact on the conclusion? Nope. That’s because  we still haven’t negated the basis of the conclusion . All that we know is that there are other parameters that TOO can determine what this particular parameter determines. So what? Does that take away from the fact that the use of scientific methods is enough to determine whether parapsychology is a genuine science- Nope!  The conclusion is still valid .

So you see, the Negation Test helps you arrive at the correct answer with a 100% surety; however, you must use it only after you have narrowed down to two contender choices.

To practice the Negation Test with some more assumption questions, take a CR Ability Quiz  here . The added bonus is that you get a realistic estimate of your strengths and weaknesses in CR.

Good Luck!

egmat · Answer

There are 5 Practice Problems for this article, the link to which has been given at the end of this post.

Article #2: How Do You Negate Statements? Introduction In order to negate any statement in CR, you should be familiar with the concept of logical negation and representing sample spaces on the Possibility Line. We cover all of this in our first article in the Negation Test Series : What is Negation and What are Various Sample Spaces . In this article, we will apply that understanding to master the negation of any given statement. Right then…Let’s get started! How to Negate Statements? By this time, you should be somewhat comfortable with the concept of Possibility Line and representing various sample spaces on it. Let’s follow a step-by-step approach to see how this understanding can help you negate statements easily. Step 1: Understanding the Segment The first step in negating a statement is understanding the segment the statement talks about. How do we do that? We simply understand about whom/what is the information given; for instance, if the statement says Most basket-ball players are more than six feet tall , then our segment is just basketball players and not any other kind of players - the statement gives information ONLY about basket-ball players. Step 2: Understanding the Sample Space The second step in negating a statement is understanding the sample space the statement gives information about. Now, you know that typically group-markers such as some, most, none etc. determine the sample space for the statement. Accordingly, in the current example, the sample space would be the range covered by the group marker “Most” = >50%. This sample space is basically the point/range of possibilities covered by the statement on the Possibility Line. Accordingly, let’s represent it on the Possibility Line: https://gmatclub.com/blog/wp-content/uploads/2015/06/01-e1433505777904.png Step 2: Understand the Possibilities outside the identified Sample Space This is the third and the final step in negating a statement. On the Possibility Line, determine the area that is NOT covered by the sample space/range of possibilities covered by the given statement. So, in the current example, the area that lies outside the possibilities covered by Most is Up to 50% . This is it! This is the negated space, using which we’ll create the negated statement. https://gmatclub.com/blog/wp-content/uploads/2015/06/02-e1433505919860.png *Negated space = possibilities not covered by the original sample space So far so good. But how do you write this down in the form of the negated statement? It is very simple. To derive the negated statement, you just need to replace the original group marker in the original statement, “Most” in this case, by the negated space . Let’s do this together. Original Statement: Most basket-ball player are more than six feet tall. Negated Statement: Up to 50% of basket-ball players are more than six feet tall. Simple, wasn’t it? Let’s apply the process to some more example statements. Example A Original Statement: Some farmers who live in India have adopted modern techniques in farming. Step 1 Understanding the Segment: The statement talks about a category of farmers: farmers WHO live in India. Therefore, this is our segment. Step 2 Understanding the Sample-Space: The group marker present in the statement is some. Therefore, the range of possibilities this statement talks about is 1- 100. Let’s represent it on the Possibility Line: https://gmatclub.com/blog/wp-content/uploads/2015/06/03-e1433506322390.png Step 3 Understand the possibilities OUTSIDE the sample space: As you can see in the above section, the sample space covered by some is 1-100. Therefore, we are left with only one possibility on the Possibility Line that is OUTSIDE this space – the possibility of none/no or 0 farmers who live in India. This is indeed the negated space. Let’s see it on the Possibility Line: https://gmatclub.com/blog/wp-content/uploads/2015/06/04-e1433506425832.png Let’s now deduce the negated statement by replacing the original group-marker by the negated space: Original Statement: Some farmers who live in India have adopted modern techniques in farming. Negated Statement: None of the farmers who live in India have adopted modern techniques in farming. Example B Let’s take another example, and this time we’ll evaluate some given statements to see which one fits the bill of the negated statement. Original Statement: Every individual who has taken a loan will say that EMIs are a headache. Options for negated statements: A. Not every individual who hasn’t taken a loan will say that EMIs are a headache. B. Only some individuals who have taken a loan will say that EMIs are a headache. C. No individual who has taken a loan will say that EMIs are a headache. D. At least one individual who has taken a loan will say that EMIs are a headache. E. Not every individual who has taken a loan will say that EMIs are a headache. Step 1 Understanding the Segment: The statement talks about a category of individuals: individuals WHO have taken some loan or the other. Step 2 Understanding the Sample-Space: The group marker present in the given statement is Every. Now every individual means the same as all individuals. Accordingly, let’s represent it on the Possibility Line: https://gmatclub.com/blog/wp-content/uploads/2015/06/05-e1433506642839.png Step 3 Understand the possibilities OUTSIDE the sample space: As you can see in the above section, all represents a single possibility point where each and every individual who has taken a loan will say that EMIs are a headache. So, if this segment contains 100 such individuals, then all represents the point at which all 100 will say that EMIs are a headache. Accordingly, anything that is outside this possibility point falls under the negated space. Now what is this negated space? Think about it. If we start from 0, then up till what point we do not reach all or 100? It is 99, right? So the negated space will cover the range 0-99. We can represent this on the Possibility Line in the following way: https://gmatclub.com/blog/wp-content/uploads/2015/06/06-e1433506781446.png Let’s now deduce the negated statement by replacing the original group-marker by the negated space: Original Statement: Every individual who has taken a loan will say that EMIs are a headache. Negated Statement: Not all individuals who have taken a loan will say that EMIs are a headache. Now that we know what the negated statement is, evaluating the given options should be a cakewalk. So, let’s get cracking! Answer Choice Explanation A. Not every individual who hasn’t taken a loan will say that EMIs are a headache. Incorrect – Wrong Segment This choice talks about individuals who have NOT taken a loan. We don’t need to consider it any further. B. Only some individuals who have taken a loan will say that EMIs are a headache. https://gmatclub.com/blog/wp-content/uploads/2015/06/07-e1433507090520.png Incorrect : The space covered by the option overlaps with the sample space of the given statement. Therefore, this option fails to provide the right negated space. Remember, the negated space contains only the possibilities OUTSIDE the original sample space. C. No individual who has taken a loan will say that EMIs are a headache. https://gmatclub.com/blog/wp-content/uploads/2015/06/08-e1433507182891.png Incorrect : The space covered by the option doesn’t include all the possibilities that lie outside the original sample-space. Remember, the logical negation of a statement should account for all the possibilities lying outside the sample space of the given statement. Therefore, this option cannot be the logical negation of the given statement. D. At least one individual who has taken a loan will say that EMIs are a headache. Incorrect : This is essentially the same as Option B, since saying that at least 1 person does X means the same as saying some people do X . Think about it! At least one person did X means that we know for sure that 1 out of the given segment definitely did X – the number could be more; it could be even all , but we know for sure that at least one person was involved. This gives us the same sample space as some (1-100). Therefore, this option cannot be the logical negation of the given statement. E. Not every individual who has taken a loan will say that EMIs are a headache. “Not every” is same as “Not all”. https://gmatclub.com/blog/wp-content/uploads/2015/06/09.png *not every = not all Correct : As you can see, the diagrammatic representation above matches the Possibility Line diagram we come up with before evaluating the options statements. The space covered by the option covers all the possibilities outside the possibility point denoted by all . Therefore, option E is the logical negation of the given statement. You are now ready to move to the exercise questions to check your understanding of how to negate statements. The link to the exercise questions is given below Practice Problems Try your hand at solving the problems given in the below link.

learn-how-to-negate-statements-exercise-questions-199347.html?sid=fa9fc874e9bf49946924e25e4210d73c#p1534692 Good Luck!

P.S.: The pdf of this article is attached below.

1991sehwag · Answer

Thanks for this post EGMAT kudos to you :-)

zaveriaakash · Answer

Thanks for making Negation so simple.... waiting for the 3rd article in this series....

egmat · Answer

Glad that you like the articles. Article #3 is posted now. Cheers!!

shivanigs · Answer

This set of articles is outstanding!! Hats off to you E-Gmat team :-D

P.S. - It'll be great if the article link in the course is updated with these as well

arjunmenonv · Answer

Can someone explain what is that one possibility in "This means that there is definitely one possibility that a field employs scientific methods but is still not a genuine scientific enterprise". article 3 second question.

And how is it different from statement 1: both have the same negated range.

And how is it different from statement 1: both have the same negated range.

shyind · Answer

E-gmat Very much useful. Thanks for sharing

Now that I am able to work on assumption problems.

AA2014 · Answer

great article... although im strong in CR yet this article adds to my skill set.

Thanks a lot. May I know when will Article#3 be posted?

AA2014 · Answer

I mean, when will Article#3 be posted in pdf format?

ommtomm12 · Answer

The option 1 and 2 have same negated space. So how 1 is not right and 2 is right?

Linhbiz · Answer

Thanks for the detail explanation & methodology, especially the additional points to exclude option choice

(Y)

sairam595 · Answer

Dear  egmat

With reference to Official question Explanation in Article-3 I have below question. Please clarify.

Argument: Although parapsychology is often considered a pseudoscience, it is in fact a genuine scientific enterprise, for it uses scientific methods such as controlled experiments and statistical tests of clearly stated hypotheses to examine the questions it raises.
The conclusion above is properly drawn if which of the following is assumed?

A. Every genuine scientific enterprise has to use scientific methods to examine the questions it raises.
B. Any field of study that employs scientific methods is a genuine scientific enterprise.

Negated version of Choice B:

Not all fields of study that employ scientific methods are genuine scientific enterprises.

0-99 fields of study that employ scientific methods are genuine scientific enterprises.

If we consider the two extreme ones:
0 fields of study that employ scientific methods are genuine scientific enterprises. - Weakens the Conclusion
99 fields of study that employ scientific methods are genuine scientific enterprises.- Strengthens the conclusion

here you said that  "the negated version says that it is not sufficient as there is definitely 1 possibility in which even a field that uses scientific methods is not a genuine scientific enterprise"

But for similar case in option A - inplace of 99 you used " Almost ALL"  - Please explain why?

Choice A - Every genuine scientific enterprise has to use scientific methods to examine the questions it raises.

Negated version of Choice A: Not every genuine scientific enterprise has to use scientific methods to examine the questions it raises.

Rephrase of the negated statement: 0 - 99 genuine scientific enterprises have to use scientific methods to examine the questions they raise.

Impact of the negated statement on the conclusion: The negated statement offers a range of possibilities. We’ll consider the two extreme ones for a clear understanding. They are:

1. No genuine scientific enterprises has to use scientific methods to examine the questions it raises. – weakens the conclusion as it indicates that it is probably not a criterion worth considering.

2. Almost all genuine scientific enterprises have to use scientific methods to examine the questions they raise. – strengthens the conclusion, as it indicates that it is a criterion worth considering.

sairam595 · Answer

Dear  egmat ,

Could you please explain to my above query.

Prashantogs · Answer

Agree with arjunmenonv & ommtomm12. Please clarify how option1 & option2 are applying different logics?

sairam595 · Answer

Dear  egmat ,

Can you please comment on above query!

anud33p · Answer

I think  sairam595  and a couple of others indeed raise a very good point and it left me scratching my head as well.

A. Every genuine scientific enterprise has to use scientific methods to examine the questions it raises.
B. Any field of study that employs scientific methods is a genuine scientific enterprise.

As per your discussion, both of these yield similar logical negatives but different conclusions are drawn. In my humble opinion, I think you have treated the logical negative of  anything  incorrectly. I believe the logical opposite of anything is nothing. Case in point - Anything is fine! I think the logical opposite, in this case coincides with the polar opposite = Nothing.

While that is just my hypothesis, if we use ^ this to draw the logical negative, that would separate options A and B and show why the logical negative of B would significantly weaken the author's conclusion.

@e-gmat,  daagh ,  AjiteshArun

anud33p · Answer

Irrespective, Thank you for this elaborate explanation of logical negatives. I am struggling with Assumptions and while I know assumption negation is a good technique, I am not applying it properly, especially in cases like option 3 here:

How should I negate  (C) Any enterprise that does not use controlled experiments and statistical tests is not genuine science. 
No enterprise that does not use controlled experiments and statistical tests is not genuine science?

I wish they had demonstrated this technique on a complex statement like this one. Anyway, can some of the experts please weigh on how to negate such statements?  AjiteshArun ,  daagh ,  GMATNinja , @e-gmat

Here is the original demo question with the prompts.
Argument: Although parapsychology is often considered a pseudoscience, it is in fact a genuine scientific enterprise, for it uses scientific methods such as controlled experiments and statistical tests of clearly stated hypotheses to examine the questions it raises.

The conclusion above is properly drawn if which of the following is assumed?

(A) If a field of study can conclusively answer the questions it raises, then it is a genuine science.
(B) Since parapsychology uses scientific methods, it will produce credible results.
 (C) Any enterprise that does not use controlled experiments and statistical tests is not genuine science. 
(D) Any field of study that employs scientific methods is a genuine scientific enterprise.
(E) Since parapsychology raises clearly statable questions, they can be tested in controlled experiments.

AjiteshArun · Answer

Maybe it'd help if we looked at that statement like this:

Any enterprise that does not use X is not Y.  ← This means that X is  necessary  (but not necessarily  sufficient ) for Y. In other words, the lack of X is enough to say "not Y", but the presence of X is not enough to say "Y".

If we want to say that X is  not  necessary for Y, we could do so like this:

Not all enterprises that do not use X are not Y.  ← This means that there is  at least one  "not X" that is a "Y".

We  don't  want to say something like this:

No enterprise that does not use X is not Y.   ← This would mean that "not X" is enough to say "Y".

Negation Test Series: Article #1 - Understand Negation & Sample Spaces

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