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

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Article: What and How to negate (6 Exercise questions) [#permalink] New post 07 Sep 2012, 09:02
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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.

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

Image


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



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.

Image

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

Image

Image


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.

Image

Image

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

Image

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

Image

Take Away: It is sometimes possible to negate by either negating the subject of an answer choice or by negating the Verb.


Image


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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Last edited by egmat on 31 Jul 2013, 11:10, edited 6 times in total.
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 07 Sep 2012, 16:45
Thank you for the article. This is the most comprehensive coverage of the negation test. Even through I probably need to read the article again, I already feel more confident. I will try to take the stab at a few questions.

Example 1 is quite challenging. Here is my response.

Ex1: Correct choice = Choice a/Choice f
I noted that you changed the verb and it was quite challenging

Ex2: Choice A and choice D
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 07 Sep 2012, 21:21
Superb article. Was very helpful in providing insight on the negation of an assumption.
Following are my takes for the examples:
Ex1: f
Ex2: a and d
Ex3: a
Ex4: a and b

Thanks
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 07 Sep 2012, 23:14
I have a doubt:


Quote:
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


Some GMAT test takers who take the exam after 1 month of preparation do not perform better than they did in their first mock.
I think that it means that 0 test taker did perform better on their mock. But we required that 0 to 99 should perform well.

All perform well ----- 100 perform well
Some perform well ---- 1 to 100, inclusive, perform well
Some did not perform well ---- 0 perform well

so the negation, according to me will be:
All GMAT test takers who take the exam after 1 month of preparation
did not perform better than they did in their first mock


Please clarify!!

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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 08 Sep 2012, 01:10
Great article.

But I guess I will take some time to get used to it since it's new to me.

Question 1 is confusing to me: My answer choices:

Q1) A (E and F are confusing to me, don't feel that they are correct, but not sure)
Q2) A
Q3) A
Q4) A and D
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 08 Sep 2012, 05:31
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Quote:
Some perform well ---- 1 to 100, inclusive, perform well
Some did not perform well ---- 0 perform well


@Rahul if some perform well => 1 to 100 perform well (which is correct) then some did not perform well should be 1 to 100 did not perform well. Does that make sense and address your doubt. Just think about it and let me know.

Others: There are some good responses but I am looking for rigor. This is more of quant that CR and with so many quant gurus here, I am looking forward to some more analysis. also dont forget to attend tomorrow's session. I will discuss the answers in tomorrow's session.

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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 08 Sep 2012, 07:05
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) This means 51-100 perform 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 do not perform well ~~ This Negates
b) All GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock. 100 perform well ~~ This is incorrect
c) No GMAT test taker who takes the exam after 1 month of preparation performs better than they did in their first mock. 0 perform well ~~ This is incorrect
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. 51-100 perform well ~~ This is same as the stimulus
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. 0-50 perform well ~~ This negates
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. 0-50 do not perform well ~~ This is incorrect. But is this same as stimulus??
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. 0-100 do not perform well ~~ This is incorrect


so according to me A and E are correct. Please confirm

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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 08 Sep 2012, 07:26
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Ex2: Every internet dating profile in the world begs for some spontaneity (Multiple answers may be correct) This means 100
a) Not every internet dating profile in the world begs for some spontaneity 0-99 ~~ Negates :-D
b) No internet dating profile in the world begs for some spontaneity 0 ~ Incorrect
c) Most internet dating profiles in the world begs for some spontaneity 51-100 ~~ Incorrect
d) Some internet dating profiles in the world do not beg for some spontaneity 1-100 ~~ Incorrect



Ex3: Innovations such as iPhone happen nowhere outside Apple. (Multiple answers may be correct) This means 1

a) Innovations such as iPhone do happen outside Apple. >1 ~~ Negates :-D
b) Innovations such as iPhone do not happen outside Apple. 1 ~~ same as stimulus
c) No other company is as innovative as Apple is. 1 ~~ SAME as stimulus
d) Innovations such as iPhone happen both inside Apple and in other companies. >= 1 ~~ Negates :-D



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) This means 0

a) Some sane people who have never given a ride to a stranded passenger will give a ride to someone dressed in a hood 1-100 ~~ Negates :-D
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 1-100 ~~ Negates :-D
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 ~~ incorrect
d) No sane person who has ever given a ride to a stranded passenger will give a ride to someone dressed in a hood. ~~ Incorrect
e) Some sane people who have given a ride to a stranded passenger will give a ride to someone dressed in a hood ~~ incorrect

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Last edited by ExuberantRahul on 09 Sep 2012, 21:09, edited 4 times in total.
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 08 Sep 2012, 16:50
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Hi Guys,

Thank you for your responses. Here are some of the answers. Rahul gets Kudos for trying :)

Ex1. Choice A is not correct. Can anyone justify why that is the case. Hint - draw the number line. Choices E & G are correct.
Ex2: Choice A is correct and so is choice D.
Ex 3. Can someone tell me the difference between choice A and Choice D.
Ex 4: To be continued :)

Again, I would like to see some (more) analysis. We will discuss these examples in the free session tomorrow. Register to get the invite.

See you tomorrow.

-Rajat

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Last edited by egmat on 08 Sep 2012, 17:46, edited 3 times in total.
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 08 Sep 2012, 17:39
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Prashant1984 wrote:
Superb article. Was very helpful in providing insight on the negation of an assumption.
Following are my takes for the examples:
Ex1: f
Ex2: a and d
Ex3: a
Ex4: a and b

Thanks
Prashant


Dear Prashant. Example 1, Choice F. What sample space does choice f occupy. What does it mean when you say that up to half the test takers do not perform better.

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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 09 Sep 2012, 10:43
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Here is the recording of CR2-Prethinking for Assumptions. Log in to your e-GMAT account to view the full recording of the free session. View the help video below for details.




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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 09 Sep 2012, 17:17
This article is good. It said about "some" and "negation" which are misunderstood many times.

When do we have the Part 2 of this article?
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 09 Sep 2012, 17:59
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Dear Mr thang. I am glad you like the article. I will add the point 2 after we get some responses to the questions posted. I look forward to your response.

Rajat

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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 09 Sep 2012, 18:56
Ex-1
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. ----- In this choice 51 - 100 did not perform well. But this does not include all the negation. Will require 49 -100 to not do well if this statement has to negate the original statement.

Ex-3
Ex3: Innovations such as iPhone happen nowhere outside Apple. (Multiple answers may be correct)

a) Innovations such as iPhone do happen outside Apple.
d) Innovations such as iPhone happen both inside Apple and in other companies.

Innovation Inside Apple –
Ex 3 refers to inside this area. So negation will be anything outside this area

Not (outside) Apple –
Choice A covers this area as it states innovation happen outside apple. This is outside of the innovation inside apple area

Choice D – states Inside Apple + Outside Apple which is the whole area– This statement includes the statement plus the negation
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 11 Sep 2012, 17:17
egmat wrote:
Ex 3. Can someone tell me the difference between choice A and Choice D.
Ex 4: To be continued :)
-Rajat


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

Ex-4: A and B are equivalent and correct. C considers only "ALL" case. D and E are incorrect because we did not negated the verb but changed the definition of the person being considered i.e. in effect we modified the sample space.
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 17 Sep 2012, 22:01
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vikram4689 wrote:

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.

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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 17 Sep 2012, 22:06
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Here are couple of more fresh questions:

Ex-5: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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Last edited by egmat on 18 Sep 2012, 20:19, edited 1 time in total.
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 18 Sep 2012, 05:44
egmat wrote:
vikram4689 wrote:

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.

i did not get your question. it seems you are asking something else because i mentioned the difference in my last post OR may be my reasoning is incorrect. please explain your question
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 18 Sep 2012, 05:57
egmat wrote:
Here are couple of more fresh questions:

Ex-5: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 did not get 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.


5. every writer will tell (100) -> negation -> not every writer will tell (0-99) -> this implies -> (1-100) writer will not tell -> some writer will not tell (B) only

6. we are concerned only with people who ARE sick so eliminate D,E,F. 100 people did not get vaccinated -> negation -> 0-99 people did not get vaccinated OR 1-100 did get vaccinated. B and C refer to 1-100 did not get vaccinated. A negates both subject and verb, so cannot be correct. All seem incorrect, please tell what is wrong in my reasoning.
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Re: Article: What and How to negate (4 Exercise questions) [#permalink] New post 18 Sep 2012, 16:55
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Dear Vikram,

I appreciate your diligent approach. Here is a clue to Ex 6. I have reproduced Ex-6 below.

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


Can you write the above as

Everyone who became sick did not get vaccinated. . This means that if 100 people became sick, then none of them got vaccinated. What would be the negation of this?

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.".

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Last edited by egmat on 17 Dec 2013, 03:25, edited 3 times in total.
Re: Article: What and How to negate (4 Exercise questions)   [#permalink] 18 Sep 2012, 16:55
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