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Educator: Reducing class sizes in our school district would require

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Educator: Reducing class sizes in our school district would require [#permalink]

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Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are underqualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement.

Which one of the following is an assumption required by the educator’s argument?

(A) Class sizes in the school district should be reduced only if doing so would improve overall student achievement.
(B) At least some qualified teachers in the school district would be able to improve the overall achievement of students in their classes if class sizes were reduced.
(C) Students place a greater value on having qualified teachers than on having smaller classes.
(D) Hiring more teachers would not improve the achievement of any students in the school district if most or all of the teachers hired were underqualified.
(E) Qualified teachers could not be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs.

Source: LSAT
[Reveal] Spoiler: OA

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 22 Aug 2017, 15:13
How can the OA be "E". I chose "D" because of the below understanding. Please provide the OE for the same. Awaiting your reply.

Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are underqualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement.

Which one of the following is an assumption required by the educator’s argument?

(A) Class sizes in the school district should be reduced only if doing so would improve overall student achievement. -This is just restating what is given in the conclusion.
(B) At least some qualified teachers in the school district would be able to improve the overall achievement of students in their classes if class sizes were reduced. -This is a fact set
(C) Students place a greater value on having qualified teachers than on having smaller classes. -Students don't put a greater value on having qualified teachers.
(D) Hiring more teachers would not improve the achievement of any students in the school district if most or all of the teachers hired were underqualified. -This bridges the gap in the conclusion correctly.
(E) Qualified teachers could not be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs. -Irrelevant. The argument is about student achievement and teacher's qualification. This option captures only one point.
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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 23 Aug 2017, 00:08
Masshole wrote:
Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are underqualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement.

Which one of the following is an assumption required by the educator’s argument?

(A) Class sizes in the school district should be reduced only if doing so would improve overall student achievement.
(B) At least some qualified teachers in the school district would be able to improve the overall achievement of students in their classes if class sizes were reduced.
(C) Students place a greater value on having qualified teachers than on having smaller classes.
(D) Hiring more teachers would not improve the achievement of any students in the school district if most or all of the teachers hired were underqualified.
(E) Qualified teachers could not be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs.

Source: LSAT


Can you please provide the OE, Masshole
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Educator: Reducing class sizes in our school district would require [#permalink]

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New post 23 Aug 2017, 02:01
Hello GMATNinja mikemcgarry, Could you please throw some light on this LAST question. I am unable to comprehend the reason behind OA.

Awaiting your response,

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 23 Aug 2017, 02:49
Quote:
Assumption—SN. The correct answer choice is (E)

Your task in this Assumption question is to select the answer containing information required for the
educator’s conclusion that reducing class sizes in the district would probably not improve overall
student achievement. The argument, reordered for clarity, proceeds:

..... Premise: ..... students receive more individualized instruction when classes are smaller

..... Premise: reducing class sizes in our school district would require hiring more teachers

..... Premise: ..... however, there is already a shortage of qualified teachers in the region

..... Premise: ..... and, education suffers when teachers are underqualified

..... Conclusion: ..... thus, reducing class sizes in our district would probably not improve overall
..... ..... ..... ..... student achievement

There are two different approaches to this question, each of which yields a strong prephrase,
though only one is tested. One prephrase is that the idea of student achievement was not previously
mentioned in the premises, and it is not inherently the case that greater individualized instruction
produces improved overall student achievement. Therefore, in one sense your prephrase is that this is
a Supporter style Assumption question, and that the correct answer may provide information linking
the idea of individualized instruction with overall student achievement.

On the other hand, this argument also has another logical gap distinct from the new information in
the conclusion, and so could be a Defender type Assumption question, in which the correct answer
will raise a potential objection to the conclusion in order to dismiss it, thus defending the conclusion.

A logical gap in this argument is that the conclusion that reducing class sizes would probably not
improve overall student achievement is supported only by the premise that education suffers when
teachers are underqualified. However, there is no indication elsewhere in the argument that any
teacher currently in the district is underqualified. While a premise establishes that there is a shortage
of teachers in the region, nothing in the argument states that only teachers in the region can be hired.
Therefore, an alternative prephrase is that the answer choice may defend the conclusion against the
possibility that teachers may be hired from outside the region.

The incorrect answers will not contain information required for the conclusion to be valid. Instead,
the information in those choices may support the conclusion while not be required for it to be valid,
may have no effect on the conclusion, or may weaken it.

Answer choice (A): The conclusion involved a probabilistic prediction about what will occur, and
not an opinion about what should or should not occur. Therefore, this premise regarding a principle
is not material to the conclusion and has no effect on it.

Answer choice (B): If some qualified teachers would be able to improve the overall acheivement of
students in their classes, then it becomes less likely reducing class sizes would not improve over all
student achievement, so this information undermines the conclusion.

Answer choice (C): This choice has no effect on the conclusion, because student preference was
irrelevant to the conclusion.

Answer choice (D): While this information would strengthen the conclusion, it is unnecessarily
restrictive and therefore not required for the conclusion to be valid.

Answer choice (E): This is the correct answer choice. This information raises the possibility
discussed in the Defender related prephrase, that teachers may be hired from outside the region. If
this choice were logically negated, meaning that qualified teachers could be persuaded to move into
the region, then the conclusion would be invalid.

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 23 Aug 2017, 05:26
Masshole wrote:
Assumption—SN. The correct answer choice is (E)

Your task in this Assumption question is to select the answer containing information required for the
educator’s conclusion that reducing class sizes in the district would probably not improve overall
student achievement. The argument, reordered for clarity, proceeds:

..... Premise: ..... students receive more individualized instruction when classes are smaller

..... Premise: reducing class sizes in our school district would require hiring more teachers

..... Premise: ..... however, there is already a shortage of qualified teachers in the region

..... Premise: ..... and, education suffers when teachers are underqualified

..... Conclusion: ..... thus, reducing class sizes in our district would probably not improve overall
..... ..... ..... ..... student achievement

There are two different approaches to this question, each of which yields a strong prephrase,
though only one is tested. One prephrase is that the idea of student achievement was not previously
mentioned in the premises, and it is not inherently the case that greater individualized instruction
produces improved overall student achievement. Therefore, in one sense your prephrase is that this is
a Supporter style Assumption question, and that the correct answer may provide information linking
the idea of individualized instruction with overall student achievement.

On the other hand, this argument also has another logical gap distinct from the new information in
the conclusion, and so could be a Defender type Assumption question, in which the correct answer
will raise a potential objection to the conclusion in order to dismiss it, thus defending the conclusion.

A logical gap in this argument is that the conclusion that reducing class sizes would probably not
improve overall student achievement is supported only by the premise that education suffers when
teachers are underqualified. However, there is no indication elsewhere in the argument that any
teacher currently in the district is underqualified. While a premise establishes that there is a shortage
of teachers in the region, nothing in the argument states that only teachers in the region can be hired.
Therefore, an alternative prephrase is that the answer choice may defend the conclusion against the
possibility that teachers may be hired from outside the region.

The incorrect answers will not contain information required for the conclusion to be valid. Instead,
the information in those choices may support the conclusion while not be required for it to be valid,
may have no effect on the conclusion, or may weaken it.

Answer choice (A): The conclusion involved a probabilistic prediction about what will occur, and
not an opinion about what should or should not occur. Therefore, this premise regarding a principle
is not material to the conclusion and has no effect on it.

Answer choice (B): If some qualified teachers would be able to improve the overall acheivement of
students in their classes, then it becomes less likely reducing class sizes would not improve over all
student achievement, so this information undermines the conclusion.

Answer choice (C): This choice has no effect on the conclusion, because student preference was
irrelevant to the conclusion.

Answer choice (D): While this information would strengthen the conclusion, it is unnecessarily
restrictive and therefore not required for the conclusion to be valid.

Answer choice (E): This is the correct answer choice. This information raises the possibility
discussed in the Defender related prephrase, that teachers may be hired from outside the region. If
this choice were logically negated, meaning that qualified teachers could be persuaded to move into
the region, then the conclusion would be invalid.


The aforesaid explanation just says that option D is restrictive. We can't just say this and dismiss the answer choice.
The OE is a total waste. Also, the explanation seems as if the author knew that the answer is "E" and then he started pouring in the points to convince the reader that answer is E.
GMATNinja mikemcgarry please kindly throw some light on this question.

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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gmatexam439 wrote:
The aforesaid explanation just says that option D is restrictive. We can't just say this and dismiss the answer choice.
The OE is a total waste. Also, the explanation seems as if the author knew that the answer is "E" and then he started pouring in the points to convince the reader that answer is E.
GMATNinja mikemcgarry please kindly throw some light on this question.

Regards

Dear gmatexam439,

I'm happy to respond. :-)

My friend, I assume you are familiar with the Negation Test, one of the best ways to identify assumptions. I will use that here. Since you ask about (D) vs. (E), I simply will discuss those two.

Here's the prompt argument:
Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are underqualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement.

With the negation test, we want to negate the candidate for assumptions and see what effect this negative statement has on the argument. If negating a statement devastates an argument, completely tears it down, then the positive version of that statement is the assumption.

Here's (D)
(D) Hiring more teachers would not improve the achievement of any students in the school district if most or all of the teachers hired were underqualified.
I've highlighted the words that make me suspicious. I believe this is what the aforementioned explanation meant by "restrictive."
One possible negation of (D):
Hiring more teachers would improve the achievement of exactly one student in the school district if most or all of the teachers hired were underqualified.
So if one student clearly benefits and no one else besides this single student benefits, then that is certainly not particularly cheerful news. In general, the argument remains the same: the experience of one outlier students does not change the general predictions for what will happen to the vast majority of students.
We can negate (D) and the negation doesn't invalidate the argument, so (D) is not an assumption.

Once again, it's very important to understand the subtle semantics here.
general: Hiring underqualified teachers would not improve the achievement of the students.
restrictive: Hiring underqualified teachers would not improve the achievement of any students.
The first is a general statement about what will happen to the majority of students—most will not improve, but perhaps a few odd exceptions to the norm will. That's a perfectly realistic statement. The second is much more stringent restriction, claiming that not one single student would improve. This latter statement smacks of extremism and dogmatism. Any argument that claims a 100% effect is particularly vulnerable to objection.

Here's (E):
(E) Qualified teachers could not be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs.
The negation of this is straightforward.
(E) Qualified teachers can be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs
If this is true, it absolutely obliterates the argument. Education quality is not going to suffer at all, because scores and scores of qualified teachers will be flooding the region. There is no way to maintain the original argument if the negation of (E) is a fact.
Negating choice (E) completely destroys the argument, so this is clearly an assumption.

Does all this make sense?
Mike :-)
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Educator: Reducing class sizes in our school district would require [#permalink]

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New post 23 Aug 2017, 19:46
Masshole wrote:
Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are under qualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement

Which one of the following is an assumption required by the educator’s argument?

(D) Hiring more teachers would not improve the achievement of any students in the school district if most or all of the teachers hired were under qualified.
(E) Qualified teachers could not be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs.



The question stem states would probably not improve overall student achievement.
Option stem D goes one step beyond and states would not improve for anyone. This need not be true. May be one student's performance increases and other person's decreases. Again, net effect or overall achievement remains the same.
E is a much better option because the question states that lack of qualified teachers in the region makes it impossible t implement the plan.

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 24 Aug 2017, 00:50
mikemcgarry wrote:
Dear gmatexam439,

I'm happy to respond. :-)

My friend, I assume you are familiar with the Negation Test, one of the best ways to identify assumptions. I will use that here. Since you ask about (D) vs. (E), I simply will discuss those two.

Here's the prompt argument:
Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are underqualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement.

With the negation test, we want to negate the candidate for assumptions and see what effect this negative statement has on the argument. If negating a statement devastates an argument, completely tears it down, then the positive version of that statement is the assumption.

Here's (D)
(D) Hiring more teachers would not improve the achievement of any students in the school district if most or all of the teachers hired were underqualified.
I've highlighted the words that make me suspicious. I believe this is what the aforementioned explanation meant by "restrictive."
One possible negation of (D):
Hiring more teachers would improve the achievement of exactly one student in the school district if most or all of the teachers hired were underqualified.
So if one student clearly benefits and no one else besides this single student benefits, then that is certainly not particularly cheerful news. In general, the argument remains the same: the experience of one outlier students does not change the general predictions for what will happen to the vast majority of students.
We can negate (D) and the negation doesn't invalidate the argument, so (D) is not an assumption.

Once again, it's very important to understand the subtle semantics here.
general: Hiring underqualified teachers would not improve the achievement of the students.
restrictive: Hiring underqualified teachers would not improve the achievement of any students.
The first is a general statement about what will happen to the majority of students—most will not improve, but perhaps a few odd exceptions to the norm will. That's a perfectly realistic statement. The second is much more stringent restriction, claiming that not one single student would improve. This latter statement smacks of extremism and dogmatism. Any argument that claims a 100% effect is particularly vulnerable to objection.

Here's (E):
(E) Qualified teachers could not be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs.
The negation of this is straightforward.
(E) Qualified teachers can be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs
If this is true, it absolutely obliterates the argument. Education quality is not going to suffer at all, because scores and scores of qualified teachers will be flooding the region. There is no way to maintain the original argument if the negation of (E) is a fact.
Negating choice (E) completely destroys the argument, so this is clearly an assumption.

Does all this make sense?
Mike :-)



Dear mikemcgarry

Can you please show why B is wrong? I do not know how to negate when using 'if sentence'

Thanks

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 24 Aug 2017, 09:07
mikemcgarry wrote:
gmatexam439 wrote:
The aforesaid explanation just says that option D is restrictive. We can't just say this and dismiss the answer choice.
The OE is a total waste. Also, the explanation seems as if the author knew that the answer is "E" and then he started pouring in the points to convince the reader that answer is E.
GMATNinja mikemcgarry please kindly throw some light on this question.

Regards

Dear gmatexam439,

I'm happy to respond. :-)

My friend, I assume you are familiar with the Negation Test, one of the best ways to identify assumptions. I will use that here. Since you ask about (D) vs. (E), I simply will discuss those two.

Here's the prompt argument:
Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are underqualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement.

With the negation test, we want to negate the candidate for assumptions and see what effect this negative statement has on the argument. If negating a statement devastates an argument, completely tears it down, then the positive version of that statement is the assumption.

Here's (D)
(D) Hiring more teachers would not improve the achievement of any students in the school district if most or all of the teachers hired were underqualified.
I've highlighted the words that make me suspicious. I believe this is what the aforementioned explanation meant by "restrictive."
One possible negation of (D):
Hiring more teachers would improve the achievement of exactly one student in the school district if most or all of the teachers hired were underqualified.
So if one student clearly benefits and no one else besides this single student benefits, then that is certainly not particularly cheerful news. In general, the argument remains the same: the experience of one outlier students does not change the general predictions for what will happen to the vast majority of students.
We can negate (D) and the negation doesn't invalidate the argument, so (D) is not an assumption.

Once again, it's very important to understand the subtle semantics here.
general: Hiring underqualified teachers would not improve the achievement of the students.
restrictive: Hiring underqualified teachers would not improve the achievement of any students.
The first is a general statement about what will happen to the majority of students—most will not improve, but perhaps a few odd exceptions to the norm will. That's a perfectly realistic statement. The second is much more stringent restriction, claiming that not one single student would improve. This latter statement smacks of extremism and dogmatism. Any argument that claims a 100% effect is particularly vulnerable to objection.

Here's (E):
(E) Qualified teachers could not be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs.
The negation of this is straightforward.
(E) Qualified teachers can be persuaded to relocate in significant numbers to the educator’s region to take teaching jobs
If this is true, it absolutely obliterates the argument. Education quality is not going to suffer at all, because scores and scores of qualified teachers will be flooding the region. There is no way to maintain the original argument if the negation of (E) is a fact.
Negating choice (E) completely destroys the argument, so this is clearly an assumption.

Does all this make sense?
Mike :-)


Dear mikemcgarry,

Thank you for your quick reply, and thank you for always patiently explaining the details of a question. However, I have a doubt in the above explanation. Please correct me where am I going wrong:

My Understanding
While using the negation technique, don't we just negate the main verb of the sentence ? In the aforesaid negation provided by you, we are actually changing the object of the sentence.

For example: If I say, "John can play with any of his cars". The negation of this sentence would be "John can't play with any of his cars" rather than "John can't play with one of his cars". We are just changing the meaning here.
Likewise, in our question at hand wouldn't correct negation be "Hiring more teachers would not improve the achievement of any number of students in the school district if most or all of the teachers hired were under-qualified". Now, if we read this statement this is also killing the argument.

Please correct me where am I going wrong? I have been using the negation technique for some time now and have never come across a negation in which we are changing the object itself. We always have to focus on the main verb.

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 24 Aug 2017, 09:37
Mo2men wrote:
Dear mikemcgarry

Can you please show why B is wrong? I do not know how to negate when using 'if sentence'

Thanks


Hello Mo2men, I am no expert, but let me give it a shot.

Educator: Reducing class sizes in our school district would require hiring more teachers. However, there is already a shortage of qualified teachers in the region. Although students receive more individualized instruction when classes are smaller, education suffers when teachers are underqualified. Therefore, reducing class sizes in our district would probably not improve overall student achievement.
Which one of the following is an assumption required by the educator’s argument?

(B) At least some qualified teachers in the school district would be able to improve the overall achievement of students in their classes if class sizes were reduced.
Even if we have some additional qualified teachers, it doesn't mean that the OVERALL achievement would improve.
For example:
Current Scenario:
# of students=2000
# of teachers=50
Each teacher is currently looking after 40 students at a time. Now if reduce the size of this pool of students from 40 to 20, and we add 5 more qualified teachers in the pool of teachers, then it would mean that Total students who would be taught by qualified teachers would be 55*20 =1100. This means that 900 students would be taught by under-qualified teachers. Thus the situation of students is much worse now.

We need to look after overall student development -> That's the crux of the argument.

Hope that helps.
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Mo2men wrote:
Dear mikemcgarry

Can you please show why B is wrong? I do not know how to negate when using 'if sentence'

Thanks

Dear Mo2men,

How are you, my friend? I'm happy to respond. :-)

First of all, just a bit of formal logic. You would need this for the LSAT, though not typically for the GMAT.
The logical statement If P, then Q is equivalent to (not P) OR (Q).
We negate an "or" statement by changing it to an "and" statement and changing the valence of each term.
The negation would be (P) AND (not Q). That would be the formal negation to the statement "If P, then Q."

That's hypertechnical. In practice, many "if . . .then" statements can be re-worded as "all" or "every" statements, which are easy to negate.

Here's (B).
At least some qualified teachers in the school district would be able to improve the overall achievement of students in their classes if class sizes were reduced.

The opposite of "at least some" is "none."
Negation of (B)
Not even one qualified teacher in the school district would be able to improve the overall achievement of students in her classes if class sizes were reduced.

Yes, this would be consistent with the bleak picture painted by the argument. It certainly doesn't challenge the conclusion of the argument in any way.

Rather than use the Negation Test, I would say a far better way to eliminate (B) would be to recognize its essential irrelevance. The central problem in the argument is having not enough qualified teachers. It's taken for granted that qualified teachers would do a good job, but there aren't enough of them. (B) kinda tells us what we already know and are taking for granted.

Does this make sense?
Quote:
Dear mikemcgarry,

Thank you for your quick reply, and thank you for always patiently explaining the details of a question. However, I have a doubt in the above explanation. Please correct me where am I going wrong:

My Understanding
While using the negation technique, don't we just negate the main verb of the sentence ? In the aforesaid negation provided by you, we are actually changing the object of the sentence.

For example: If I say, "John can play with any of his cars". The negation of this sentence would be "John can't play with any of his cars" rather than "John can't play with one of his cars". We are just changing the meaning here.
Likewise, in our question at hand wouldn't correct negation be "Hiring more teachers would not improve the achievement of any number of students in the school district if most or all of the teachers hired were under-qualified". Now, if we read this statement this is also killing the argument.

Please correct me where am I going wrong? I have been using the negation technique for some time now and have never come across a negation in which we are changing the object itself. We always have to focus on the main verb.

Regards

Dear gmatexam439,

I'm happy to respond. :-)

My friend, negating the main verb is often the correct way to negate a statement, especially if it's a very simple sentence, but it's not correct in certain special cases. In particular, when there are quantity qualifiers (e.g. all, none, most, some, always, never, sometimes, everywhere, nowhere, some places, , etc.) then these have their own rules for negation.

All do ==> opposite = some don't or at least one doesn't
None do ==> opposite = some do or at least one does
It always happens ==> opposite = Sometimes it doesn't happen
It never happens ==> opposite = Sometimes it actually does happen

You run into trouble if you simply negate the main verb. You would change "All do" to "All don't," and that's not a true opposite.
Every polygon is a triangle. = a false statement
Just negating the main verb gives us
Every polygon is not a triangle. = another false statement
In formal logic, the true negation of a false statement should be a true statement. If we turn one false statement into an other false statement, we've done something wrong. The true opposite of the original would be
Not every polygon is a triangle = a true statement

Does all this make sense?
Mike :-)
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Magoosh Test Prep

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Re: Educator: Reducing class sizes in our school district would require [#permalink]

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New post 25 Aug 2017, 05:58
mikemcgarry wrote:
Dear gmatexam439,

I'm happy to respond. :-)

My friend, negating the main verb is often the correct way to negate a statement, especially if it's a very simple sentence, but it's not correct in certain special cases. In particular, when there are quantity qualifiers (e.g. all, none, most, some, always, never, sometimes, everywhere, nowhere, some places, , etc.) then these have their own rules for negation.

All do ==> opposite = some don't or at least one doesn't
None do ==> opposite = some do or at least one does
It always happens ==> opposite = Sometimes it doesn't happen
It never happens ==> opposite = Sometimes it actually does happen

You run into trouble if you simply negate the main verb. You would change "All do" to "All don't," and that's not a true opposite.
Every polygon is a triangle. = a false statement
Just negating the main verb gives us
Every polygon is not a triangle. = another false statement
In formal logic, the true negation of a false statement should be a true statement. If we turn one false statement into an other false statement, we've done something wrong. The true opposite of the original would be
Not every polygon is a triangle = a true statement

Does all this make sense?
Mike :-)


Dear mikemcgarry,

That last example made a lot of sense. Thank you very much for the insight. I will correct myself and use the negation technique correctly.

Regards
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