Learn How to Negate Statements: Exercise Questions

Identify the correct negations for the following statements.

1. Most websites that are developed with a proper focus on SEO get a significant number of visitors.

a. 49% of the websites that are developed without a proper focus on SEO get a significant number of visitors. outside the segment
b. All websites that are developed with a proper focus on SEO get a significant number of visitors. overlap sample space
c. Some websites that are developed with a proper focus on SEO get a significant number of visitors. overlap sample space
d. Up to 50% of the websites that are developed without a proper focus on SEO get a significant number of visitors. outside the segment

I am unable to find the correct answer choice because as per my understanding all a/b/c/d are incorrect 


2. Some people over 60 years of age are conservative investors.

a. Not all people over 60 years of age are conservative investors.
b. No person over the age of 60 is a conservative investor. CORRECT
c. Not everyone over 60 is a conservative investor.
d. Most people are conservative investors.



3. Up to 70% of the laptops powered by HCD processor are prone to over-heating issues.

a. Not every laptop powered by HCD processor is prone to over-heating issues.
b. Some laptops that are not powered by HCD processor are prone to over-heating issues.
c. 70% or more laptops powered by HCD processor are prone to over-heating issues.
d. More than 70% laptops powered by HCD processor are prone to over-heating issues. CORRECT


4. Any GMAT taker will agree that the GMAT is a mentally gruelling exam.

a. Only some GMAT takers will agree that the GMAT is a mentally gruelling exam.
b. Not more than half of the GMAT takers will agree that the GMAT is a mentally gruelling exam.
c. Not every GMAT taker will agree that the GMAT is a mentally gruelling exam. CORRECT
d. No GMAT taker will agree that the GMAT is a mentally gruelling exam.

Ans to the questions are as follows
1 d
2 b
3 d
4 c

There was a typo in one of the options. It has been corrected now. Thank you for pointing it out.

egmat can you please post the solutions & the explanations.

1. Most websites that are developed with a proper focus on SEO get a significant number of visitors.
Most represent 51-100, therefore, we need to negate in a such way, so the segment described does not overlap with the segment given (0-50 or up to 50%)
a. 49% of the websites that are developed without a proper focus on SEO get a significant number of visitors. - this talks about different websites
b. All websites that are developed with a proper focus on SEO get a significant number of visitors. - All = 100. This set overlaps with the set given (most 51-100).
c. Some websites that are developed with a proper focus on SEO get a significant number of visitors. Again an overlap. Some - 1-100.
d. Up to 50% of the websites that are developed with a proper focus on SEO get a significant number of visitors. - Correct Choice

 


2. Some people over 60 years of age are conservative investors.
Some - 1-100. We need to find an answer choice that has to present 0 people.
a. Not all people over 60 years of age are conservative investors. - not all means 0-99. This might be tempting, but it is incorrect. We need an answer choice that gives 0 only.
b. No person over the age of 60 is a conservative investor. - correct. No person = 0.
c. Not everyone over 60 is a conservative investor. - not everyone is the same as not all (A). This is incorrect.
d. Most people are conservative investors. - Most is 51-100. This is again incorrect.



3. Up to 70% of the laptops powered by HCD processor are prone to over-heating issues.
The scope is laptops powered. We need to find a segment that does not overlap with 0-70.
a. Not every laptop powered by HCD processor is prone to over-heating issues. Not every = 0-99. This is incorrect.
b. Some laptops that are not powered by HCD processor are prone to over-heating issues. Some = 1-100. This is incorrect.
c. 70% or more laptops powered by HCD processor are prone to over-heating issues. This might be tempting, but it is an overlap. we need to have an answer choice with >70%.
d. More than 70% laptops powered by HCD processor are prone to over-heating issues. This is the correct answer choice.


4. Any GMAT taker will agree that the GMAT is a mentally gruelling exam.
Ok, what does any mean? Some or All? In my understanding, it represents all. Whoever you ask, from the GMAT takes, he/she will tell you that GMAT is a mentally gruelling exam. In this case, we need to find an answer choice that contradicts this. The best option is not all (0-99).
a. Only some GMAT takers will agree that the GMAT is a mentally gruelling exam. - only some 1-100. We have an overlap.
b. Not more than half of the GMAT takers will agree that the GMAT is a mentally gruelling exam. - Not more than half 0-50 -> again overlap.
c. Not every GMAT taker will agree that the GMAT is a mentally gruelling exam. - Not every, hm, that's good. 0-99. That means that at least someone will not say the same.
d. No GMAT taker will agree that the GMAT is a mentally gruelling exam. - This is a tempting answer choice, if you think that Any=Some. Any=1-100, and No = 0. But this is not what we are looking for.

Can Egmat please post the answers

Hi egmat
Kindly post the answers to the above questions.

Hi chetan2u

You are moderator of course and you know more than me, but just for purpose to explain e-gmat's logic and help other students I want to clarify something.

In the 4th question you say that every answer is possible because they mean {not 100%}. But according to e-gmat the logical negation of a statement should account for all the possibilities lying outside the sample space of the given statement. Therefore, other options cannot be the "perfect negation" though they negate the sentence.




For students who want to learn more about negation refer to the link below :

https://gmatclub.com/forum/negation-test-series-article-1-understand-negation-sample-spaces-198821.html

Hi egmat,

Can you please help in posting the answer of this question? Though all over the thread, C is the most opted choice but I don't think so. As per my understanding the correct answer should be D.

4. Any GMAT taker will agree that the GMAT is a mentally gruelling exam.
a. Only some GMAT takers will agree that the GMAT is a mentally gruelling exam.
b. Not more than half of the GMAT takers will agree that the GMAT is a mentally gruelling exam.
c. Not every GMAT taker will agree that the GMAT is a mentally gruelling exam.
d. No GMAT taker will agree that the GMAT is a mentally gruelling exam.

My Analysis --
Segment -- GMAT taker (Not any other taker, for example, GRE taker etc etc.. are all irrelevant)
Sample Space -- ANY (As per my understanding, ANY means ALL or ANY PART of the group)

So, logically the correct answer should be D and NOT C.

Please help me in knowing the correct answer?

P.S. My reasoning of ANY versus EVERY is based on the article on the following link,
https://english.stackexchange.com/questions/77058/what-is-the-difference-between-anyone-and-everyone-in-this-context

Thanks.
-Varun

Hi...

Sorry .. just saw your reply
The Q is about accepted LOGIC and not Someone's logic.
Any of gmattaker means everyone will follow a certain line.
So if you can prove that ATLEAST one will not follow the line, you are negating the original reasoning or sentence.

This is what each of the four choices is doing. So all can weaken the main sentence.

Identify the correct negations for the following statements.

1. Most websites that are developed with a proper focus on SEO get a significant number of visitors.

a. 49% of the websites that are developed without a proper focus on SEO get a significant number of visitors.
b. All websites that are developed with a proper focus on SEO get a significant number of visitors.
c. Some websites that are developed with a proper focus on SEO get a significant number of visitors.
d. Up to 50% of the websites that are developed with a proper focus on SEO get a significant number of visitors.

 


2. Some people over 60 years of age are conservative investors.

a. Not all people over 60 years of age are conservative investors.
b. No person over the age of 60 is a conservative investor.
c. Not everyone over 60 is a conservative investor.
d. Most people are conservative investors.



3. Up to 70% of the laptops powered by HCD processor are prone to over-heating issues.

a. Not every laptop powered by HCD processor is prone to over-heating issues.
b. Some laptops that are not powered by HCD processor are prone to over-heating issues.
c. 70% or more laptops powered by HCD processor are prone to over-heating issues.
d. More than 70% laptops powered by HCD processor are prone to over-heating issues.


4. Any GMAT taker will agree that the GMAT is a mentally gruelling exam.

a. Only some GMAT takers will agree that the GMAT is a mentally gruelling exam.
b. Not more than half of the GMAT takers will agree that the GMAT is a mentally gruelling exam.
c. Not every GMAT taker will agree that the GMAT is a mentally gruelling exam.
d. No GMAT taker will agree that the GMAT is a mentally gruelling exam.

Hi chetan2u,

Can you please explain the difference between ANY and EVERY? I am really confused between the two.

Thanks in advance!

Thanks.
-Varun

The solution is marked in RED:

Identify the correct negations for the following statements.

1. Most websites that are developed with a proper focus on SEO get a significant number of visitors.

a. 49% of the websites that are developed without a proper focus on SEO get a significant number of visitors.
b. All websites that are developed with a proper focus on SEO get a significant number of visitors.
c. Some websites that are developed with a proper focus on SEO get a significant number of visitors.
d. Up to 50% of the websites that are developed with a proper focus on SEO get a significant number of visitors.

 


2. Some people over 60 years of age are conservative investors.

a. Not all people over 60 years of age are conservative investors.
b. No person over the age of 60 is a conservative investor.
c. Not everyone over 60 is a conservative investor.
d. Most people are conservative investors.



3. Up to 70% of the laptops powered by HCD processor are prone to over-heating issues.

a. Not every laptop powered by HCD processor is prone to over-heating issues.
b. Some laptops that are not powered by HCD processor are prone to over-heating issues.
c. 70% or more laptops powered by HCD processor are prone to over-heating issues.
d. More than 70% laptops powered by HCD processor are prone to over-heating issues.


4. Any GMAT taker will agree that the GMAT is a mentally gruelling exam.

a. Only some GMAT takers will agree that the GMAT is a mentally gruelling exam.
b. Not more than half of the GMAT takers will agree that the GMAT is a mentally gruelling exam.
c. Not every GMAT taker will agree that the GMAT is a mentally gruelling exam.
d. No GMAT taker will agree that the GMAT is a mentally gruelling exam.

egmat coud you please clarify how to negate options with double nots
and with most?

GMATNinja coud you please clarify how to negate options with double nots
and with most?

Hi chetan2u

In Q 4 , choice A says only some and some means anything b/w 1-100 so how can we say that this can be correct ans choice.?
Is it due to the addition of "Only " before some that is making all the difference. please help

It seems someone deleted my earlier response to this question in an old post of mine, so posting again..

1. Most websites that are developed with a proper focus on SEO get a significant number of visitors.
So we have to look for a choice that tells us that NOT most, that is \(\leq{50%}\) websites that are developed with a proper focus on SEO get a significant number of visitors.

a. 49% of the websites that are developed without a proper focus on SEO get a significant number of visitors.
The websites being talked of are different, so out of scope
b. All websites that are developed with a proper focus on SEO get a significant number of visitors.
Strengthens
c. Some websites that are developed with a proper focus on SEO get a significant number of visitors.
Number could be 49, 50 or 75
d. Up to 50% of the websites that are developed with a proper focus on SEO get a significant number of visitors.
So exactly 50%...Correct
ans D
 


2. Some people over 60 years of age are conservative investors.

a. Not all people over 60 years of age are conservative investors.
b. No person over the age of 60 is a conservative investor.
c. Not everyone over 60 is a conservative investor.
d. Most people are conservative investors.
Clearly the answer is B



3. Up to 70% of the laptops powered by HCD processor are prone to over-heating issues.

a. Not every laptop powered by HCD processor is prone to over-heating issues.
b. Some laptops that are not powered by HCD processor are prone to over-heating issues.
c. 70% or more laptops powered by HCD processor are prone to over-heating issues.
d. More than 70% laptops powered by HCD processor are prone to over-heating issues.
Only D gives a clear range above 70%, opposite of the statement.


4. Any GMAT taker will agree that the GMAT is a mentally gruelling exam.
This clearly means 100% or all, so we look for something that tells us NOT 100%

a. Only some GMAT takers will agree that the GMAT is a mentally gruelling exam.
Only some MEANS there are others who will not agree..Correct
b. Not more than half of the GMAT takers will agree that the GMAT is a mentally gruelling exam.
Again this tells us that not all 100% will agree... Correct
c. Not every GMAT taker will agree that the GMAT is a mentally gruelling exam.
Again this tells us that not all 100% will agree... Correct
d. No GMAT taker will agree that the GMAT is a mentally gruelling exam.
Thus 0%, so not 100%..Correct

Here all the choices are sufficient to negate the original sentence.
ans ABCD