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Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a

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Magoosh GMAT Instructor
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 20 Mar 2017, 11:35
LakerFan24 wrote:
Sorry mikemcgarry, I don't buy your take on the "and" vs. "or". This answer/explanation is blasphemous IMO. I know we're not "allowed" to say that the GMAC/GMAT is trying to trick us, but let's spare the political correctness.
> There SHOULD be a meaning error here b/c if I am talking about a specific canal (let's call it Canal X) that is 40 ft wide AND 12 ft deep, this canal WILL BE DIFFERENT than another one (i.e. Canal Y) that is 40 ft wide OR 12 ft deep. That is, if a canal is 40ft wide AND 12ft deep, there is no way it can ALSO be 40ft wide OR 12ft deep.

There is no escaping this logic

Dear LakerFan24,

I'm happy to respond. :-)

We are getting into some very tricky regions of formal logic at this point. First, I will represent this symbolically. Let P and Q be general factual statements, that may be true or false.
The logical opposite of (P and Q) is (not P or not Q).
The logical opposite of (P or Q) is (not P and not Q).

(P and Q) includes just one case: (P = true, Q = true)
The opposite, (not P or not Q), includes the other three possibilities
(a) (P = false, Q = true)
(b) (P = true, Q = false)
(c) (P = false, Q = false)

(P or Q) includes just one case:
(a) (P = true, Q = true)
(b) (P = false, Q = true)
(c) (P = true, Q = false)
The opposite, (not P and not Q), just the last possibility: (P = true, Q = false)

The connector word (and/or) flip-flop from whether you are making statements in the affirmative or in the negative. Notice that the statements in the prompt are negatives, and your statements were in the affirmative. That is an excellent way to get confused on what the right connector world would be.

Thus:
It is legal to drive when one is sober AND has vision (i.e. is not blind).
It is not legal to drive when one is drunk OR blind.

This is the verbal equivalent of multiplying both sides of the "equation" by a negative: here, the "equals sign" is the verb "to be," and the negative of the "AND" statement is the "OR statement.

I would urge you to look at this old question (GMAT OG13, SC #21)
https://gmatclub.com/forum/the-commission-has-directed-advertisers-to-restrict-the-use-63645.html

Does all this make sense?
Mike :-)
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 21 Mar 2017, 15:03
mikemcgarry wrote:
LakerFan24 wrote:
Sorry mikemcgarry, I don't buy your take on the "and" vs. "or". This answer/explanation is blasphemous IMO. I know we're not "allowed" to say that the GMAC/GMAT is trying to trick us, but let's spare the political correctness.
> There SHOULD be a meaning error here b/c if I am talking about a specific canal (let's call it Canal X) that is 40 ft wide AND 12 ft deep, this canal WILL BE DIFFERENT than another one (i.e. Canal Y) that is 40 ft wide OR 12 ft deep. That is, if a canal is 40ft wide AND 12ft deep, there is no way it can ALSO be 40ft wide OR 12ft deep.

There is no escaping this logic

Dear LakerFan24,

I'm happy to respond. :-)

We are getting into some very tricky regions of formal logic at this point. First, I will represent this symbolically. Let P and Q be general factual statements, that may be true or false.
The logical opposite of (P and Q) is (not P or not Q).
The logical opposite of (P or Q) is (not P and not Q).

(P and Q) includes just one case: (P = true, Q = true)
The opposite, (not P or not Q), includes the other three possibilities
(a) (P = false, Q = true)
(b) (P = true, Q = false)
(c) (P = false, Q = false)

(P or Q) includes just one case:
(a) (P = true, Q = true)
(b) (P = false, Q = true)
(c) (P = true, Q = false)
The opposite, (not P and not Q), just the last possibility: (P = true, Q = false)

The connector word (and/or) flip-flop from whether you are making statements in the affirmative or in the negative. Notice that the statements in the prompt are negatives, and your statements were in the affirmative. That is an excellent way to get confused on what the right connector world would be.

Thus:
It is legal to drive when one is sober AND has vision (i.e. is not blind).
It is not legal to drive when one is drunk OR blind.

This is the verbal equivalent of multiplying both sides of the "equation" by a negative: here, the "equals sign" is the verb "to be," and the negative of the "AND" statement is the "OR statement.

I would urge you to look at this old question (GMAT OG13, SC #21)
https://gmatclub.com/forum/the-commission-has-directed-advertisers-to-restrict-the-use-63645.html

Does all this make sense?
Mike :-)



With all due respect, I've read your entire post looking for a direct answer to my question and was unable to find one. To reiterate, if you told me to find a canal that is 40ft wide AND 12 ft deep, and then later you tell me to find another canal that is 40ft wide OR 12ft deep, there is absolutely no way I could find one canal satisfies both of your requirements. In the end, I would find one canal for each of your 2 conditions, leaving you with a total of two different canals. This is why I say the meaning changed.

Does my argument make sense?
Magoosh GMAT Instructor
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 21 Mar 2017, 17:00
LakerFan24 wrote:
With all due respect, I've read your entire post looking for a direct answer to my question and was unable to find one. To reiterate, if you told me to find a canal that is 40ft wide AND 12 ft deep, and then later you tell me to find another canal that is 40ft wide OR 12ft deep, there is absolutely no way I could find one canal satisfies both of your requirements. In the end, I would find one canal for each of your 2 conditions, leaving you with a total of two different canals. This is why I say the meaning changed.

Does my argument make sense?

Dear LakerFan24,

I'm happy to respond. :-)

I see now. You misunderstand the word "or" itself. See this post:
The Word “Or” in GMAT Math

You see, in most ordinary colloquial speech, the word "or" is used as the exclusive or (written XOR in logic)
P XOR Q means P by itself or Q by itself but definitely not both together and definitely not neither

In all of mathematics on planet Earth, and through the GMAT, the word "or" is used exclusively as the inclusive or; in logic and mathematics, this is represented by the ordinary word "or."
P or Q mean P by itself or Q by itself or PQ together but definitely not neither.

Thus, in the logical use of the word, I would be an example of both
(a) a man who is a college graduate AND a NY Mets fan
(b) a man who is a college graduate OR a NY Mets fan
I am definitely not an example of
(c) a man who is a college graduate XOR a NY Mets fan
In fact, by definitely, any person in (c) could not be in (a), and vice versa. All true, but wherever "or" appears on the GMAT or in any math book on the planet, it never never never means XOR. On the GMAT, OR is always inclusive, and (a) is a strict logical subset of (b).

Does all this make sense?
Mike :-)
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 21 Mar 2017, 17:17
mikemcgarry wrote:
LakerFan24 wrote:
With all due respect, I've read your entire post looking for a direct answer to my question and was unable to find one. To reiterate, if you told me to find a canal that is 40ft wide AND 12 ft deep, and then later you tell me to find another canal that is 40ft wide OR 12ft deep, there is absolutely no way I could find one canal satisfies both of your requirements. In the end, I would find one canal for each of your 2 conditions, leaving you with a total of two different canals. This is why I say the meaning changed.

Does my argument make sense?

Dear LakerFan24,

I'm happy to respond. :-)

I see now. You misunderstand the word "or" itself. See this post:
The Word “Or” in GMAT Math

You see, in most ordinary colloquial speech, the word "or" is used as the exclusive or (written XOR in logic)
P XOR Q means P by itself or Q by itself but definitely not both together and definitely not neither

In all of mathematics on planet Earth, and through the GMAT, the word "or" is used exclusively as the inclusive or; in logic and mathematics, this is represented by the ordinary word "or."
P or Q mean P by itself or Q by itself or PQ together but definitely not neither.

Thus, in the logical use of the word, I would be an example of both
(a) a man who is a college graduate AND a NY Mets fan
(b) a man who is a college graduate OR a NY Mets fan
I am definitely not an example of
(c) a man who is a college graduate XOR a NY Mets fan
In fact, by definitely, any person in (c) could not be in (a), and vice versa. All true, but wherever "or" appears on the GMAT or in any math book on the planet, it never never never means XOR. On the GMAT, OR is always inclusive, and (a) is a strict logical subset of (b).

Does all this make sense?
Mike :-)



Ah - completely understand. I didn't really think about "exclusive" or "inclusive" or, but you're right. I feel like in Probability problems, the "inclusive" or can be highlighted, whereas if someone says "Mike, you won a new car OR a new house", the "exclusive" or is taken into effect.

Now to clarify -- you're saying the "inclusive" version of "or" occurs on both the Quant AND Verbal sections? So every time I see an "or" on the GMAT, I am to assume the inclusive property?
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 22 Mar 2017, 10:16
LakerFan24 wrote:
Ah - completely understand. I didn't really think about "exclusive" or "inclusive" or, but you're right. I feel like in Probability problems, the "inclusive" or can be highlighted, whereas if someone says "Mike, you won a new car OR a new house", the "exclusive" or is taken into effect.

Now to clarify -- you're saying the "inclusive" version of "or" occurs on both the Quant AND Verbal sections? So every time I see an "or" on the GMAT, I am to assume the inclusive property?

Dear LakerFan24,

My friend, I'm happy to respond. :-)

Yes, in spoken language, the word "or" often means the exclusive "or"--especially when emotional inflection lands on that word! (I'll let you think about examples in emotionally charged interpersonal situations!)

On the GMAT Quant (and conventionally through mathematics in general), the word "or" is always inclusive. To be consistent--and the GMAT is nothing if not logically consistent!--if the unadorned word "or" appears on the Verbal or IR or even the AWA, the GMAT always would intend it as the inclusive "or." If, under some circumstances they intended the exclusive "or," they would have to spell that out explicitly (e.g. "P or Q individually, but not both together"). You are 100% safe if you assume, barring explicit language to the contrary, that every "or" you see on the GMAT is inclusive.

Does all this make sense?
Mike :-)
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 17 Jul 2017, 11:55
Although mikemcgarry clearly rules on this question with some brilliant answers out there. I would like to add a quick note from my side.

Mike I know you have clarified the confusion between "and" and "or" I am still not getting it completely, may be because it's just the way, we non-natives have been using till date.

Coming back to the question. Let's begin the answer analysis.

A. Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles across the rugged wilderness of upstate New York, the Erie Canal connected

- ",but it ran" is illogical and hence the sentence is not parallel with the modifier "Seldom more than 40 feet wide and 12 feet deep"

B. Seldom more than 40 feet wide or 12 feet deep but running 363 miles across the rugged wilderness of upstate New York, the Erie Canal connected

- CORRECT
- Usage of verb "connected" is correct


C. It was seldom more than 40 feet wide and 12 feet deep, and ran 363 miles across the rugged wilderness of upstate New York, but the Erie Canal, connecting

- Missing verb as the word "connecting" is used, making the sentence fragment.

D. The Erie Canal was seldom more than 40 feet wide or 12 feet deep and it ran 363 miles across the rugged wilderness of upstate New York, which connected

- usage of "which" is ambigous

E. The Erie Canal, seldom more than 40 feet wide and 12 feet deep, but running 363 miles across the rugged wilderness of upstate New York, connecting

- Missing verb as the word "connecting" is used, making the sentence fragment.

Hence, Answer is B

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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 14 Sep 2017, 13:45
Although "B" is a correct choice. I wanted to know if someone else can throw a few convincing points about WHY A and C are incorrect? Thanks.
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 14 Sep 2017, 14:17
AnubhavK wrote:
Although "B" is a correct choice. I wanted to know if someone else can throw a few convincing points about WHY A and C are incorrect? Thanks.



Hello AnubhavK,

I will be glad to help you out with one. :-)

Let's take a look at Choice A:

Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles across the rugged wilderness of upstate New York, the Erie Canal connected

This choice is incorrect for two reasons:

i. The sentence presents two features of Erie canal that should be parallel to each other - the width and depth of the canal and the length or the extent of stretch of the canal. Although logically parallel, the two features Seldom more than 40 feet wide and 12 feet deep and it ran 363 miles across the rugged wilderness of upstate New York are grammatically not parallel because the former is a phrase while the latter is a clause.

ii. Comma + but ids followed by an independent clause it ran... which is connected to another independent clause the Erie Canal connected... by just a comma. This structure is not grammatical.


Now let's take a look at Choice C:

It was seldom more than 40 feet wide and 12 feet deep, and ran 363 miles across the rugged wilderness of upstate New York, but the Erie Canal, connecting

This choice is also incorrect for two reason:

i. There is no verb for the subject the Erie Canal.

ii. Use of connector and instead of but takes away the intended contrast mentioned in the original sentence.


Hope this helps. :-)
Thanks.
Shraddha
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a  [#permalink]

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New post 14 Sep 2017, 14:42
ydmuley wrote:
Although mikemcgarry clearly rules on this question with some brilliant answers out there. I would like to add a quick note from my side.

Mike I know you have clarified the confusion between "and" and "or" I am still not getting it completely, may be because it's just the way, we non-natives have been using till date.




Hello ydmuley,

I would like to present my two cents on the usage of and Vs. but in this official sentence. :-)

The sentence presents a few features of the Erie Canal. This canal ran 363 miles across the upstate New York. But it is not imperative that the canal was 40 feet wide AND 12 feet deep at the same time all across the stretch. At some places it were 40 feet wide, and some places it was not. Similarly, at some places it was 12 feet deep, but not that deep at most of the places.


So it is not that the Erie Canal was seldom 40 deep wide and 12 feet deep at the same time as conveyed by the usage of and. These two conditions did not occur together. It's not that where the canal was 40 feet wide, it was 12 feet deep also. It was any one condition all along the stretch. Hence, use of or makes more sense in the context of this sentence.


Hope this helps. :-)
Thanks.
Shraddha
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Re: Seldom more than 40 feet wide and 12 feet deep, but it ran 363 miles a &nbs [#permalink] 14 Sep 2017, 14:42

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