SOLUTION
1. Most websites that are developed with a proper focus on SEO get a significant number of visitors.Negation of most (greater than 50%) is less than or equal to 50%.a. 49% of the websites that are developed without a proper focus on SEO get a significant number of visitors.
Websites developed without a proper focus on SEO is what is being talked about. Incorrect.
b. All websites that are developed with a proper focus on SEO get a significant number of visitors.
All comes under the range greater than 50% /most. Hnce it cannot be the negation, since the rest of the statement is the same. Incorrect.c. Some websites that are developed with a proper focus on SEO get a significant number of visitors.
Some signifies the range #1 to ALL Most is a subset of Some, therefore this too cannot be the right negation.d. Up to 50% of the websites that are developed with a proper focus on SEO get a significant number of visitors.Correctly refers to the negated space of "most". Correct answer! 2. Some people over 60 years of age are conservative investors.Some can be #1 to ALL. So, the only thing that lies outside this sample space is 0.a. Not all people over 60 years of age are conservative investors.
Not all could be anything from zero to ALL-1. This overlaps with the range of Some. Hence this cannot be the right answer.b. No person over the age of 60 is a conservative investor.This correctly refers to the negative space, which consists of only zero. Hence this is the correct answer!c. Not everyone over 60 is a conservative investor.
Not everyone is the same as Not all. Therefore, this option conveys the same meaning as option A.d. Most people are conservative investors.
"Most" is a subset in the range of "Some". Hence it cannot be the negation.3. Up to 70% of the laptops powered by HCD processor are prone to over-heating issues.Negation of up to 70% (0 to 70%) is more than 70%(>70%) a. Not every laptop powered by HCD processor is prone to over-heating issues.
'Not every' could mean anything from 0 to one less than the total number of laptops powered by HCD. This is a range that spans inside and outside the question statement. Hence this cannot be the right answer.b. Some laptops that are not powered by HCD processor are prone to over-heating issues.
Laptops that are not powered by HCD are not our concern here. Therefore, this is incorrect.c. 70% or more laptops powered by HCD processor are prone to over-heating issues.
The range expressed here is 70% to ALL, both ends included. Inclusion of 70% makes it overlap with the range of the question statement. Hence it cannot be the correct answer. d. More than 70% laptops powered by HCD processor are prone to over-heating issues.This statement expresses the negative space of the given statement accurately. Hence this is the correct answer!4. Any GMAT taker will agree that the GMAT is a mentally gruelling exam. "Any GMAT test taker will agree" implies that even if you pick one at random, that person will agree. So, each and every person has to agree for this statement to be true. That means Any essentially conveys the same meaning as ALL. If we change the sentence to mean at least one person exists who do not agree to the given matter, then we get the negation of this statement. a. Only some GMAT takers will agree that the GMAT is a mentally gruelling exam.
Only some is not different from exactly some, which means strictly in the 1 to ALL bracket. Since ALL is a part of this sample space, we cannot say that this is a negation of the question statement. b. Not more than half of the GMAT takers will agree that the GMAT is a mentally gruelling exam.
Not more than half of the test takers means up to 50% of the test takers. It does not cover the entire negative space of ALL. That means we do not have any information about the range from above 50% to 1 less than ALL here. Hence, we cannot say this is the correct negation of the given statement. c. Not every GMAT taker will agree that the GMAT is a mentally gruelling exam. This statement covers the range 0 to ALL-1. Therefore, this is a correct negation to the statement in question. d. No GMAT taker will agree that the GMAT is a mentally gruelling exam.
When we say not even one will agree is the negation, we ignore the possibility for any number of test takers from one to ALL-1 agreeing. Therefore, it does not cover the entire negative space. Hence this cannot be the right answer either. _________________