Article: What and How to negate (6 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



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.



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





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.





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



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



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

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.