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

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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 05 Aug 2014, 21:40
egmat wrote:
umeshpatil wrote:
Hi eGMAT,

This is really amazing article. Can you help me negation technique for below example ?

Studies have shown that a large percentage of car accidents are caused by aggressive driving. To help reduce the number of accidents and to promote traffic safety in general, insurance companies have begun to issue discounts to drivers who take defensive driving courses. Research shows that people who practice defensive driving are considerably less likely to get into a car accident. Therefore, the insurance company’s plan should help reduce the number of accidents.
Assuming the statements above are true, which of the following can be inferred from them?
A. The majority of accidents are caused by drivers who possess insurance.
B. People who manage to consistently avoid car accidents are likely practicing defensive driving.
C. Young males and other demographics known for disproportionately being involved in car accidents are less likely to practice defensive driving than other demographics.
D. An individual who does not practice defensive driving is always more likely to get into a car accident than an individual who does practice defensive driving.
E. Discounts are the most effective way for insurance companies to promote defensive driving.

Answer is C.


Hi Umesh,

The article talks about applying negation test to assumption questions. However, as you are probably thinking, the same can be applied in Inference (Must be true) questions as well.

In this case, if you negate option C, it becomes:

Young males and other demographics known for disproportionately being involved in car accidents are more likely to practice defensive driving than other demographics.

Now, this would directly go against the information presented in the passage:

Research shows that people who practice defensive driving are considerably less likely to get into a car accident

Can you see how these two statements are contradicting? or Should I elaborate more here?

Thanks,
Chiranjeev


How about negating option D ?
An individual who does practice defensive driving is always more likely to get into a car accident than an individual who does NOT practice defensive driving.

Isn't this also going against the argument ?

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Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 23 Aug 2014, 05:19
Hi e-gmat,

My query purports to the question number 6.

As per the concept file, we should define the universal sample space.

Here
Ex-6: All the people who became sick did not get vaccinated.

WHO tells us that universal sample space to be considered is "People who became sick".

Then how to evaluate answer options 4,5, and 6.

My analysis:

100 people who became sick : No vaccination.

Negation if subject is negated:

(A). Not all [0-99](sick)-> No vaccination

Negation if verb is negated:

(B). All people[100] (sick)-> vaccination.

(1).Not everyone who became sick got vaccinated.
[0-99]->vaccination --Doesn't match with (A) or (B)
(2).Some people who became sick did not get vaccinated
[1-100]-> no vaccination --Doesn't match with (A) or (B)
(3).At least one person who became sick got vaccinated
[1-100]->vaccinated--Doesn't match with (A) or (B)
How this option is correct?

I don't know how to evaluate below options since as per the question the universal sample space is "People who got sick".
All people who got vaccinated did not become sick
Most people who did not become sick got vaccinated
Most people who did not get vaccinated did not become sick.

Please advice.
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Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 23 Sep 2014, 10:16
egmat wrote:
ankitD wrote:
Hi,

I am confused about the first and second questions

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.

I understand that E and G are correct but my doubt is with choice A
choice A says that 51-100 takers did not perform better or 0-50 did perform better
Now question says that 51-100 performed better or 0-50 did not perform better so isn't choice A negating the question.

I know I am missing a piece of info here but just cannot get it sad

Hi Ankit,

Interesting doubts.

Look at the highlighted portion above.

Let's look at your analysis of choice A: It mean 51-100 did not perform OR 0-50 did perform

Are both the sets consistent? If I say, 50 performed - would that be in line with choice A? The answer is No. Because choice A says a majority did not perform. So, the lowest number who did not perform well is 51 and therefore, the highest number that performed well is 49 and not 50.

So, choice A actually means either 51-100 did not perform or 0-49 did perform. (Another way to look at it is that the sum of both the sets have to be 100 (total number of takers), so 51+49 = 100 and 100+0=100)

Now, if you look at the original sentence, it means 51-100 performed or 0-49 did not perform.
So, the negation of original sentence is 0-50 did not perform or 50-100 did perform.

Now, look at option A - isn't it different?

ankitD wrote:


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

I get that a and d are correct answer choices but I was wondering why can't B be correct isn't that also falling under the sample space of 0-99.


No means "zero". Why do you think that No means 0-99.

If I say, no one has every slapped President Obama. What does this mean?

Hope this helps.

Thanks,
Chiranjeev



Please refer to the colored lines above.
I am not clear about the following fact regarding Ex.1;
If the original sentence means 51-100 performed or 0-49 did not perform why the negation of this sentence would not be 51-100 did not perform or 0-49 did perform?

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Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 19 Oct 2014, 20:04
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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,
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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 05 Dec 2015, 02:44
egmat wrote:


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

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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 05 Dec 2015, 06:07
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.
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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 05 Dec 2015, 13:14
Mahmud6 wrote:
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 :)

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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 29 Apr 2016, 07:01
vikram4689 wrote:
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.



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
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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 29 Apr 2016, 07:03
yaddict wrote:
ex 5
100 - tell hence negation is (0-99) tell =>(100 -{ 0-99} ) not tell = (1-100) not tell ie some will not tell
(a) 100 not tell
(b) 1-100 not tell
(c) 0 tell => 100-0 not tell = 100 not tell
(d) 51-100 not tell
thus b

Ex6
100 Ps not vaccinated (V) thus negation is (0-99) NV => (100-{0-99}) = 1-100 V that is Some sick P got vaccinated(V)
(a) Not everyone = (0-99) V or 1-100 NV
(b) Some = (1-100) NV
(c) Atleast one= (1-100) NV
(d) e f are about ppl who did not got sick so can withdraw any conclusion on P sick thus ofs!!
i am also not able to find any answer, can you please shed some light



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
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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 29 Apr 2016, 07:03
manpreetsinghkohli wrote:
I want to understand the answer(s) to the question:

Q. 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.

D & F are out of scope directly as the apply a reverse relationship. E is out as it talks about "most" and "most" won't apply in either of the two cases that I use below.

As far as I could understand the article we can negate this statement in two ways:
1. By using the same statement but the logical opposite of "All"
2. By using a not+verb form and changing the logical opposite of "All" accordingly.

Point 1:
This should give me the answer "Not all the people who became sick did not get vaccinated." - awkward construction but I applied the rule methodologically. where Not all is "0-99"
and if I convert this into "not+verb" form it should become: "Some peope who got sick got vaccinated" where "some" is 1-99 which means at least 1. This implies choice "C"
Point 2: Here we change the use the "not+verb" form and the sentence becomes the following before changing the logical opposite.
"All the people who became sick got vaccinated"
Now if I change the logical opposite it should become "No one who became sick got vaccinated" but choice A says "Not Everyone" instead of No one.
Which is the 2nd correct answer besides C? or does this question just have 1 right answer.

PS - It would be really great if you can iron out the gaps in my understanding that you might notice while reading my post.


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
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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 04 Jul 2016, 17:35
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?

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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 04 Jul 2016, 17:46
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?

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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 04 Jul 2016, 22:23
hyoeun87 wrote:
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?


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)
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Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 05 Jul 2016, 02:56
aniketm.87@gmail.com wrote:
hyoeun87 wrote:
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?


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

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Re: Article: What and How to negate (6 Exercise questions) [#permalink]

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New post 28 Oct 2017, 19:35
Can someone please provide the link for second part of the article ?????

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Re: Article: What and How to negate (6 Exercise questions)   [#permalink] 28 Oct 2017, 19:35

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