Article: What and How to negate (4 Exercise questions) Purpose : The purpose of this article is to help you think about negating statements so that you can apply the negation test for CR assumption questions. In this article we will look at how to negate using the set theory approach for negating statements. This article is a pre-requisite to our free session on “Prethinking for CR assumptions”. In addition, do not forget to register at e-GMAT to attempt a free quiz on negating statements. https://gmatclub.com/blog/wp-content/uploads/2012/09/Prethinking-e1347037874285.png Organization of the article : This article has three parts: 1. Introduction to Negation: In this section, we will briefly talk about what negating a statement means and why is it important. 2. Key skills for negation 3. 4 Questions We will soon be releasing a quiz containing 10 questions on this topic. Register at e-gmat to be notified as soon as the quiz is released. What is negation and negation test? To understand the above, lets take a simple argument. Every super-smart GMAT aspirant registers on GMATClub. Hence, every Harvard admit is a registered student at GMATClub. Assumption : Harvard only admits super-smart GMAT aspirants. Negation technique can be used to determine if the given answer choice is the true assumption or not. In other words, it a sure shot way to validate the answer (recommended use) or to determine whether an answer choice is an assumption https://gmatclub.com/blog/wp-content/uploads/2013/07/gmat2-banner11-e1373945998281.jpg Why does negation test work? The correct answer choice is like a missing premise. Which means that is has to be true for the conclusion to hold true. This implies that the negated version of the correct answer choice will shatter, falsify or invalidate the conclusion. Hence, once we have narrowed down our answer choice(s), we can verify it by evaluating whether the negated version really shatters the conclusion or not. If it does, then your selected choice is indeed the conclusion, otherwise not. In the example above, the negated version of the assumption could be one of the following: 1. Harvard does not only admit super-smart GMAT aspirants. 2. At least one Harvard admit is not super-smart aspirant. Ok, sounds good. How do we negate? When you think of negation, it helps to think in terms of sets. Each answer choice is “a part” of a super set. Hence, the negated statement = Super Set – Space occupied by the answer choice. Negated Statement=Super set-Space occupied by the answer choice Let’s an an examples. All GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock Q What is the super set ? Super set is the set of possibilities for GMAT takers who take the exam after one month of preparation. Let’s assume that there are 100 test takers who take the exam after 1 month of the preparation. Then there are multiple possibilities that exist for this group of test takers https://e-gmat.com/blogs/wp-content/uploads/2013/05/Celebrating-Milestones1.png 1. All 100 test takers who take the exam after 1 month of preparation perform better than they did on their first mock. 2. Not All test takers who take the exam after 1 month of preparation perform better than they did on their first mock. 3. Some Test Takers who take the exam after 1 month of preparation perform better than they did on their first mock. 4. Most test takers who take the exam after 1 month of preparation perform better than they did on their first mock. 5. Less than 50% of test takers who take the exam after 1 month of preparation perform better than they did on their first mock. 6. No test taker who takes the exam after 1 month of preparation performs better than he/she did on their first mock. https://gmatclub.com/blog/wp-content/uploads/2012/09/Number-line-1-e1347035777803.png There are a few things to note in the picture above. 1. Understand the Super Set : Note, we are only talking about a segment of population – the test takers who take the exam 1 month after preparing for their GMAT. This is our Universe or the super set. We are not concerned with test takers who take the exam after 15 days of preparation or 2 months of preparation. Words such as “Who” (user for people), “that” (animals, corporations etc.), “which” and “those” have a segmentation effect. Therefore, any answer choice that deals with choices outside this segment – the segment in which people take the exam after 1 month of preparation – is incorrect. TakeAway : Words such as Who, that, which, those etc. have a segmentation effect. 2. Understand the Sample space occupied by the choice : Once you have defined the Super set, understand the sample space occupied by the choice that you want to negate. Words such as all, none, some, most, etc. define these sample spacing. It is important to know what these words imply in terms of sample spaces. Taking the “Super Set” in discussion and assuming that it contains 100 test takers, here is what the sample spaces mean https://gmatclub.com/blog/wp-content/uploads/2012/09/Table-1-e1347036608637.png https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg 3. Understand what negation means : Negation or logical negation means that you select an answer choice that occupies the sample space that excludes the original choice. If it maps to another term above, then perfect, otherwise you may make the use of word “Not” to find the logical opposite. In the example above, the logical opposite of “All” is “Not All”. Note, that you may be tempted to use “Some” but “some” includes All (Notice, it includes 100) and hence is not the logical opposite. Here is a table of logical opposites. https://gmatclub.com/blog/wp-content/uploads/2012/09/Logical-Opposites-e1347035838680.png https://gmatclub.com/blog/wp-content/uploads/2012/09/Number-line-2-e1347036740613.png Our Original Answer choice All GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock Let’s now look at the answer choices https://gmatclub.com/blog/wp-content/uploads/2012/09/Answer-Choices-e1347035811226.png WHAT IF YOU NEGATE THE VERB? Let’s bring the Original choice again for clarity purposes. All GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock Notice, that in all the negated choices above, we did not modify the verb – perform better. Lets see what happens when we negate the verb. Consider the following negated choice Neg 1: Some GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock. What does the above answer choice mean? The answer choice implies that, out of 100 test takers, between 1 and 100 test takers did not perform better than they did in their first mock. This means that 0 to 99 test takers did perform better on their mock. This is the same is “Not all”. Hence, the above answer choice is Correct. Lets see how this happened https://gmatclub.com/blog/wp-content/uploads/2012/09/Answer-Choices-2-e1347037085794.png Take Away : It is sometimes possible to negate by either negating the subject of an answer choice or by negating the Verb. https://gmatclub.com/blog/wp-content/uploads/2013/07/gmat2-banner11-e1373945998281.jpg Exercise Sentences: Ex1 : Most GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. (Multiple answers may be correct ) a) Most GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock. b) All GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. c) No GMAT test taker who takes the exam after 1 month of preparation performs better than they did in their first mock. d) At least half of GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. e) Up to half of GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. f) Up to half of GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock. g) Half or more of GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock. Ex2 : Every internet dating profile in the world begs for some spontaneity (Multiple answers may be correct ) a) Not every internet dating profile in the world begs for some spontaneity b) No internet dating profile in the world begs for some spontaneity c) Most internet dating profiles in the world begs for some spontaneity d) Some internet dating profiles in the world do not beg for some spontaneity Ex3 : Innovations such as iPhone happen nowhere outside Apple. (Multiple answers may be correct ) a) Innovations such as iPhone do happen outside Apple. b) Innovations such as iPhone do not happen outside Apple. c) No other company is as innovative as Apple is. d) Innovations such as iPhone happen both inside Apple and in other companies. Ex4 : No sane person who has never given a ride to a stranded passenger will give a ride to someone dressed in a hood (Multiple answers may be correct) a) Some sane people who have never given a ride to a stranded passenger will give a ride to someone dressed in a hood b) At least one sane person who has never given a ride to a stranded passenger will give a ride to someone dressed in a hood c) All sane people who have never given a ride to a stranded passenger will give a ride to someone dressed in a hood d) No sane person who has ever given a ride to a stranded passenger will give a ride to someone dressed in a hood. e) Some sane people who have given a ride to a stranded passenger will give a ride to someone dressed in a hood Ex5 :Every writer will tell you: first, find a good café. (Multiple answers may be correct) A. Every writer will not tell you: first, find a good café. B. Some writers will not tell you: first, find a good café C. No writer will tell you: first, find a good café. D. Most writers will not tell you: first, find a good café. Ex-6 : All the people who became sick did not get vaccinated.(Multiple answers may be correct) A. Not everyone who became sick got vaccinated. B. Some people who became sick did not get vaccinated C. At least one person who became sick got vaccinated D. All people who got vaccinated did not become sick E. Most people who did not become sick got vaccinated F. Most people who did not get vaccinated did not become sick.

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Article: What and How to negate (6 Exercise questions)

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vikram4689

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18 Sep 2012, 21:08

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egmat

1. If "0" people who became sick did not get vaccinated, then 100 people who became sick got vaccinated or in other words, All people who became sick got vaccinated. (note: everyone either gets vaccinated or does not get vaccinated)

2. If 99 people who became sick did not get vaccinated, then 1 person who became sick got vaccinated.

Summarizing the above, Not everyone who became sick did not get vaccinated is equivalent to "1-99 people who became sick got vaccinated.". Isn't this the same as choice A.

please see from the logic 1-100 people who became sick got vaccinated which is not same as 1-99 people who became sick got

for quick checks, i follow that while negating either subject or verb can be negated. that means ONLY 1 of them MUST be negate

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18 Sep 2012, 21:26

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Dear Vikram,

Thanks for pointing out the inconsistency. I have made some edits. Lets try this question again.

-Rajat

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ex 5
100 - tell hence negation is (0-99) tell =>(100 -{ 0-99} ) not tell = (1-100) not tell ie some will not tell
(a) 100 not tell
(b) 1-100 not tell
(c) 0 tell => 100-0 not tell = 100 not tell
(d) 51-100 not tell
thus b

Ex6
100 Ps not vaccinated (V) thus negation is (0-99) NV => (100-{0-99}) = 1-100 V that is Some sick P got vaccinated(V)
(a) Not everyone = (0-99) V or 1-100 NV
(b) Some = (1-100) NV
(c) Atleast one= (1-100) NV
(d) e f are about ppl who did not got sick so can withdraw any conclusion on P sick thus ofs!!
i am also not able to find any answer, can you please shed some light

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09 Oct 2012, 19:40

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Quick question about the first example from the article:

Quote:

Every super-smart GMAT aspirant registers on GMATClub. Hence, every Harvard admit is a registered student at GMATClub.
Assumption: Harvard only admits super-smart GMAT aspirants.

I might be overthinking here, so please correct me if I am out of scope. Although every super-smart GMAT aspirant registers on GMATClub, you don't have to be a super-smart GMAT aspirant to register on GMATClub. Therefore, does the assumption here stand? Although every Harvard admin is a registered student at GMATClub, does it only have to be a super-smart GMAT aspirant member that makes it? Indeed the following assumption does not seem to shatter the conclusion above if we take the above into consideration:

Quote:

Harvard does not only admit super-smart GMAT aspirants.

Thanks.

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20 Oct 2012, 01:26

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when you publish the part 2, pls, notify in this posting so that we can follow . Thank you.

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18 Nov 2012, 20:25

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Exercise Sentences:

Ex1: Most GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. (Multiple answers may be correct) Most: 51-100 performed well. Answer should cover 0-50 performed well

a) Most GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock.51-100
b) All GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock.100
c) No GMAT test taker who takes the exam after 1 month of preparation performs better than they did in their first mock.0
d) At least half of GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock.50 -100
e) Up to half of GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. it covers 0-50 space
f) Up to half of GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock.double negation
g) Half or more of GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock.
50- 100 do not perform well

Ex2: Every internet dating profile in the world begs for some spontaneity (Multiple answers may be correct)
means 100 (all). Correct answer should cover 0-99
a) Not every internet dating profile in the world begs for some spontaneitysimilar to "not all"
b) No internet dating profile in the world begs for some spontaneity.0
c) Most internet dating profiles in the world begs for some spontaneity . 51-100
d) Some internet dating profiles in the world do not beg for some spontaneity1-100 do not beg. implies 0 beg

Ex3: Innovations such as iPhone happen nowhere outside Apple. (Multiple answers may be correct)

a) Innovations such as iPhone do happen outside Apple.
b) Innovations such as iPhone do not happen outside Apple.
c) No other company is as innovative as Apple is.
d) Innovations such as iPhone happen both inside Apple and in other companies.
answers choice are not comparable. i chose the answer because only that option (a) make sense

Ex4: No sane person who has never given a ride to a stranded passenger will give a ride to someone dressed in a hood (Multiple answers may be correct). 0. Answer should cover 1-100

a) Some sane people who have never given a ride to a stranded passenger will give a ride to someone dressed in a hood
b) At least one sane person who has never given a ride to a stranded passenger will give a ride to someone dressed in a hood
c) All sane people who have never given a ride to a stranded passenger will give a ride to someone dressed in a hood.100
d) No sane person who has ever given a ride to a stranded passenger will give a ride to someone dressed in a hood.
e) Some sane people who have given a ride to a stranded passenger will give a ride to someone dressed in a hood[/highlight]

Ex5:Every writer will tell you: first, find a good café. (Multiple answers may be correct)
Every=All= 100 will tell. Ans should cover 0-99 will tell
A. Every writer will not tell you: first, find a good café.0 will tell
B. Some writers will not tell you: first, find a good café
C. No writer will tell you: first, find a good café.
D. Most writers will not tell you: first, find a good café.

Ex-6: All the people who became sick did not get vaccinated.(Multiple answers may be correct)

A. Not everyone who became sick got vaccinated.
B. Some people who became sick did not get vaccinated
C. At least one person who became sick got vaccinated
D. All people who got vaccinated did not become sick
E. Most people who did not become sick got vaccinated
F. Most people who did not get vaccinated did not become sick.

I have highlighted my answers

WarriorGmat

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17 Jun 2013, 08:07

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why "some" does not include zero ?

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17 Jun 2013, 08:25

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Hi Warrior,

If I understand your question. 'Some' necceasrily means that at least one person holds the point of view.

If you say 'some' apples are nice - then at least one has to be nice....

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plumber250

Hi Warrior,

If I understand your question. 'Some' necceasrily means that at least one person holds the point of view.

If you say 'some' apples are nice - then at least one has to be nice....

Hi Plumber,

Thanks for replying,
What would be the result if you negate above example

"some apples are nice"

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24 Jul 2013, 06:19

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Hi,

I am confused about the first and second questions

Ex1: Most GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. (Multiple answers may be correct)

a) Most GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock.
b) All GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock.
c) No GMAT test taker who takes the exam after 1 month of preparation performs better than they did in their first mock.
d) At least half of GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock.
e) Up to half of GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock.
f) Up to half of GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock.
g) Half or more of GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock.

I understand that E and G are correct but my doubt is with choice A
choice A says that 51-100 takers did not perform better or 0-50 did perform better
Now question says that 51-100 performed better or 0-50 did not perform better so isn't choice A negating the question.

I know I am missing a piece of info here but just cannot get it sad

Ex2: Every internet dating profile in the world begs for some spontaneity (Multiple answers may be correct)
a) Not every internet dating profile in the world begs for some spontaneity
b) No internet dating profile in the world begs for some spontaneity
c) Most internet dating profiles in the world begs for some spontaneity
d) Some internet dating profiles in the world do not beg for some spontaneity

I get that a and d are correct answer choices but I was wondering why can't B be correct isn't that also falling under the sample space of 0-99.

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24 Jul 2013, 19:58

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ankitD

Hi Ankit,

Interesting doubts.

Look at the highlighted portion above.

Let's look at your analysis of choice A: It mean 51-100 did not perform OR 0-50 did perform

Are both the sets consistent? If I say, 50 performed - would that be in line with choice A? The answer is No. Because choice A says a majority did not perform. So, the lowest number who did not perform well is 51 and therefore, the highest number that performed well is 49 and not 50.

So, choice A actually means either 51-100 did not perform or 0-49 did perform. (Another way to look at it is that the sum of both the sets have to be 100 (total number of takers), so 51+49 = 100 and 100+0=100)

Now, if you look at the original sentence, it means 51-100 performed or 0-49 did not perform.
So, the negation of original sentence is 0-50 did not perform or 50-100 did perform.

Now, look at option A - isn't it different?

ankitD

Ex2: Every internet dating profile in the world begs for some spontaneity (Multiple answers may be correct)
a) Not every internet dating profile in the world begs for some spontaneity
b) No internet dating profile in the world begs for some spontaneity
c) Most internet dating profiles in the world begs for some spontaneity
d) Some internet dating profiles in the world do not beg for some spontaneity

I get that a and d are correct answer choices but I was wondering why can't B be correct isn't that also falling under the sample space of 0-99.

No means "zero". Why do you think that No means 0-99.

If I say, no one has every slapped President Obama. What does this mean?

Hope this helps.

Thanks,
Chiranjeev

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18 Sep 2013, 07:22

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What are the answers for the quiz after the article?

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21 Sep 2013, 01:12

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A very nice article on negation.

I have 2 queries:
1) I am still not able to figure out why option A in question# 1 is incorrect

2) Can we have some examples from OG on which we can apply this learning?

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egmat

Negation: Not everyone who became sick did not get vaccinated. This implies, 0-99 people who became sick did not get vaccinated.

Lets now map this space to the vaccinated space:

1. If "0" people who became sick did not get vaccinated, then 100 people who became sick got vaccinated or in other words, All people who became sick got vaccinated. (note: everyone either gets vaccinated or does not get vaccinated)

2. If 99 people who became sick did not get vaccinated, then 1 person who became sick got vaccinated.

Summarizing the above, Not everyone who became sick did not get vaccinated is equivalent to "1-100 people who became sick got vaccinated.".

At least one person who became sick got vaccinated. => 0-99 got vaccinated. Note, not everyone would be 0-99. Therefore, our negated space is 0-99 who became sick got vaccinated.

Hi e-GMAT representatives,

I was fine with till summarizing i.e, till Not everyone who became sick did not get vaccinated is equivalent to 1-100 people who became sick got vaccinated. But how did this change to 0-99 got vaccinated ?

I could deduce only two negation:
1.Not everyone(0-99) who became sick did not get vaccinated. (Subject change)
2.Some of the people(1-100) who became sick got vaccinated. (Verb change)

I am completely perplexed . Please help me clarify this.

Regards,
Nishok

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17 Dec 2013, 04:25

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nishoknm

egmat

Hi Nishok,

I agree that the last paragraph of the post does not go in line with the rest of the post. I think some inadvertent copy pasting has resulted in this. Both of your negations are correct.

I am actually going to delete the last paragraph to avoid any future confusions.

Thanks,
Chiranjeev

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06 Jan 2014, 00:12

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Hi EGmat team,

Can you please post responses for the above examples. My responses are :

1. e and g
2. a and d
3. a
4. c and d
5. a and c
6. a and b

Appreciate the quick response.
Thank you ...... you are really doing impressive job out there .

egmat

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GmatDestroyer2013

Hi,
The correct answers are:

1. e and g
2. a and d
3. a
4. a and b
5. b
6. c

Thanks,
Chiranjeev

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21 Jan 2014, 04:01

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egmat

vikram4689

Ex-3: D overlaps with the space in sample set occupied by the argument and misses some cases as it considers companies only. Hence, it is NOT equivalent to negation but A considers all the cases except those in argument and is therefore the correct answer

Dear Vikram, You are correct about example 4. For Ex -3. Look at choices A and D again. For the purposes of our discussion, is there a difference between these choices. What does "Such innovations do happen outside Apple" mean.

Hi,

In EX-3, Option (A) talks about the ALL possible region outside Apple. In other words the word "Nowhere" in the original question is negated by using the word "ALL"

For option (D), it takes a different approach where the sentence moves outside of the sample space (i.e Outside Apple) and considers INSIDE Apple space which again negates the original sentence.

Folks please share your views if my understanding on the above is correct. Thanks.

Best Regards,
Atif Jawed

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19 Feb 2014, 13:37

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Hi - Can you please validate if my analysis of this question is right?

Ex2: Every internet dating profile in the world begs for some spontaneity (Multiple answers may be correct)
a) Not every internet dating profile in the world begs for some spontaneity
b) No internet dating profile in the world begs for some spontaneity
c) Most internet dating profiles in the world begs for some spontaneity
d) Some internet dating profiles in the world do not beg for some spontaneity

Pre thinking -

Every = 100

Here the super set is " All profiles that beg for some spontaneity"
Negated Space = All (0 -100) - Every (100) = 0 - 99 profiles that beg spontaneity

Now , when 0 profile beg spontaneity, 100 do not beg spontaneity
and when 99 beg spontaneity, 1 do not beg.

The space 1 - 100 - who do not beg spontaneity can be defined by "Some"

POE :
a ) Correct - Not every (same as not all) is logical opposite of Every
b) In correct - No means zero. Doe not represent the right space
c) In correct - Most represent only 51 - 100.
d) Correct - Some is right because of reasoning stated in pre thinking

Many Thanks