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

Mahmud, I've just been fighting this topic, so I'll give you my thoughts on this.. I think that I've finally worked through all of the confusion.

The reason why Ex1 is so confusing is because 2 processes are being used here:

(1) Translating the question
(2) Negating

The two tasks are mutually exclusive processes. When translating the question, what we are really doing is figuring out the size of two sets e.g. performed better vs. not performed better. One needs to use simple addition to ensure that the sum of both of these sets equals the value of the superset (In the case of Ex 1, the superset is 100 test takers).

So when figuring out the size of the sets / translating the question “ Ex1: Most GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock", we merely use simple addition:

Size of Set 1: Most performed better = 51-100.
Size of Set 2: 51+?=100. 49. 100+?=100. 0. Thus, 0-49 did not perform better.

This is ‘translating the question’.

However, when negating, it is necessary to remember two key things (1) the formula "Negation Space = Superset - answer choice space”; (2) Ranges or values for quantity words (All/Most/None etc.) occupy 'places' on the number-line.

Lets take an example “Most performed better". Thinking about this in terms of sets. Most performed= 51-100. The superset is 'all' which is "0-100".Using the formula: Negation Space [did not perform better] = All - Most ---> (0-100) - (51-100) —> We subtract the place values of 51 through 100 from the total number of place values of “all” which are zero through 100. We are left with place values zero to 50 (0-50). We only do this when Negating.

Negation space = 0-50 did not perform better.

Back to the question. We translated the question stem (51-100 performed better, 0-49 did not perform better). We worked out the negation space for the question stem: 0-50 did not perform better. We want to now TRANSLATE this space (as we did initially when translating the original question) —> back to simple addition:

Size of Set 1: 0 - 50 did not perform better
Size of Set 2: 0+?=100. 100. 50+?=100. 50. Thus, 50 - 100 did perform better.

So the complete picture for the negation space for the question stem is: 0-50 did not perform better or 50-100 did perform better.

It is this statement to which A to G are compared. Note: we are not negating the answer choices. We are merely ‘translating’ them (using addition) and matching them to our negated question stem.

Hope this extended explanation helps. In earnest - I know that I’m going to be re-reading this at some point in the future to remind myself of the process as it is so confusing!


e-Gmat - can you confirm that my reasoning above is correct?


Cheers,
RS

I'm just going over this concept again; admittedly, it is a little confusing - even my own notes; it seems as though I have negated TWICE in my notes above, when it should be only once i.e.

Translation: 51-100 better / 0-49 not better
Negating quantity: 0-50 better / 50-100 not better

E-GMAT, can you confirm whether my reasoning in the last post is correct - or - point out any errors that I have made ? (I subscribe to your material btw).

Thanks

Negated space of perform must be ‘perform’ and vice versa.

Statement: Most Performed well ---> 51-100 performed well or 0-49 did not perform.
Negation of 51-100 performed well is 0-50 performed well, and
Negation of 0-49 did not perform is 50-100 did not perform well

So the negated statement should cover
Option (i) 0-50 performed well, or
Option (ii) 50-100 did not perform well

Negated Statement 1: Most did not perform well ---> 51-100 did not perform well (Not matched Option – i) ---> 0-49 did perform well (Not matched Option – ii). Incorrect.

Negated Statement 2: All performed well ---> 100 performed well. Incorrect.

Negated Statement 3: None performed well ---> 0 performed well. Incorrect.

Negated Statement 4: At least half performed well ---> 50-100 performed well. Incorrect.

Negated Statement 5: Up to half performed well---> 0-50 performed well. Correct. (Matched option - i)

Negated Statement 6: Up to half NOT performed well---> 0-50 Not performed well. Incorrect.

Negated Statement 7: Half or more NOT performed well---> 50-100 Not performed well. Correct. (Matched option - ii)

I also reread my above note many times.

Thanks for confirming Mahmud

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.

All (100) ………. no vaccine (-ve)
X
Not all (0-99) …….. no vaccine (-ve)

OR
No … (0) ………. vaccine (+ve)
X
Some/at-least one .. (1-99) ……. vaccine (+ve) ——> C

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.

All (100) ………. no vaccine (-ve)
X
Not all (0-99) …….. no vaccine (-ve)

OR
No … (0) ………. vaccine (+ve)
X
Some/at-least one .. (1-99) ……. vaccine (+ve) ——> C

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.

All (100) ………. no vaccine (-ve)
X
Not all (0-99) …….. no vaccine (-ve)

OR
No … (0) ………. vaccine (+ve)
X
Some/at-least one .. (1-99) ……. vaccine (+ve) ——> C

Can someone explain question number 1 again?

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.

The original: 51~100 perform better. so we need 0~50 perform better.

Why isn't a) not correct?
Most test takers do not perform better. 51~100 do not perform better. Not more than half performs better. 0~49 performs better. This is incorrect because we are missing 50?

g) 51~100 do not perform better. 0~50 perform better. What is the negation of half or more?

I do not understand how to solve question 6 at all.

There are two different verbs that can be negated and what is the true negation of all people who became sick did not get vaccinated?

Can someone explain all 6 answer choices?

negation of half or more (50 - 100) is upto half but not more than half (0 - 49)
always associate numbers with it. Its easier this way
e and g are right for this Q

Most GMAT test takers who take the exam after 1 month of preparation perform better than they did in their first mock
most => 51 - 100, do perform better -----> +ve

you can either negate most (50-100) ------> 0-49 (upto half)
OR
you can negate the verb did perform better -----> did not perform better
Do not negate both (double negation = same sentence as the original one {-*- = +}

e) Up to half (0 -49) of GMAT test takers who take the exam after 1 month of preparation perform better(+ve verb) than they did in their first mock. -----> works as it negates only the 1st part

g) Half or more (50 - 100 or most) of GMAT test takers who take the exam after 1 month of preparation do not (-ve verb) perform better than they did in their first mock. -----> negative of the verb (dont get confused with the 1st part, half or more = most = (50 -100)

Here, in the two highlighted statement range for most is different. (50-100 & 51-100). Pls explain.

I have read all the solutions and found double negation where we change Subject & verb both. While I agree, double negation leads to original sentence. But some of the answer choices are leading to the confusion due to both subject & verb change.

Lets take this example :

Ex5:Every writer will tell you: first, find a good café. (Multiple answers may be correct)

Implies : Every (100%) ..will tell => negation=> 0-99 tell => 1-100 do not tell [I understand how to reach this point, but don't we negate both subject & verb)

A. Every writer will not tell you: first, find a good café. 100% , will not tell, Negates [ I do not know why this is incorrect]
B. Some writers will not tell you: first, find a good café . 1-100.. NOT . YES. Negates

Can someone please provide the link for second part of the article ?????

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Hi, thanks for your posting and I really appreciate your kind explanation.
For the ex- 5, I still have some question, why A is incorrect, as it negated the verb. Can you elaborate on it please?
thanks again!

Ex2: Every internet dating profile in the world begs for some spontaneity (Multiple answers may be correct)
b) No internet dating profile in the world begs for some spontaneity

Why is B incorrect ?

Every internet dating profile in the world begs for some spontaneity.

100 profiles beg for 1-100 spontaneity.
Inverse, 0 profiles beg for 1-100 spontaneity OR 0-99 profiles beg for 0 spontaneity.

B states No internet dating profile in the world begs for some spontaneity.
0 profiles beg for 1-100 spontaneity. Why is this not answer? egmat

ayuG : It is incorrect because you are taking a polar opposite and not logical opposite. The logical opposite of every (meaning all 100) is not every (meaning 0-99) and not None(meaning 0).

Hope this makes sense.

Cheers
AA