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John and Fawn, each drinking at a constant pace, can finish

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John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 17 Feb 2012, 19:53
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John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

1) The average time it would take both to finish independently is 30 hours.
2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case.

This is actually from MGMAT flash cards. Looked interesting and hence I posted after modifying it a bit (I added a new statement).

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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 17 Feb 2012, 21:55
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Chembeti wrote:
John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

1) The average time it would take both to finish independently is 30 hours.
2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case.

This is actually from MGMAT flash cards. Looked interesting and hence I posted after modifying it a bit (I added a new statement).


John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

Given: 1/J + 1/F = 1/12

(1) The average time it would take both to finish independently is 30 hours --> J+F=60. Now, since we don't know which one drinks faster then even if we substitute F with 60-J (1/J + 1/(60-J) = 1/12) we must get two different answers for J and F: J<F and J>F. Not sufficient.

(2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case --> F=J-10 --> 1/J + 1/(J-10) = 1/12 --> J=4 (not a valid solution as F in this case is negative) and J=30 (F=20). Sufficient.

Now, technically the answer should be B, as Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

But even though the formal answer to the question is B, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. In our question, from (2) we have that the average time is (30+20)/2=25 and (1) states that it's 30, so the statements clearly contradict each other.

In order it to be a realistic GMAT question (1) should read: The average time it would take John to finish the case drinking alone and Fawn to finish the case drinking alone is 25 hours. In this case for (1) we'll have: 1/J + 1/(50-J) = 1/12 --> J=30 (so F=20 --> J>F) or J=20 (so F=30 --> J<F). Statements don't contradict and (1) is still insufficient.

Hope it's clear.
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 17 Feb 2012, 21:11
Hi,

I think the OA is incorrect. I think it should be D

Statement 1 : Each takes 30 hours to finish the case independently => John can finish a case in 30 hours hence sufficient
Statement 2 : J = F+10

1/J + 1/F = 1/12

1/(F+10) + 1/F = 1/12

Solving the quadratic equation we get F = 20 / F =-6. Work time problem hence -6 is eliminated

Hence we can find J

Hence Statement 2 is sufficient

Hence D
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 17 Feb 2012, 21:20
Statement 1 can't be correct because you don't know who out of the 2 is the faster drinker... John could drink faster than his friend or vice versa. Also you definition of average is wrong... Average mean A+B/2. A and B does not have to be the same. It could take John 50 mins to finish and Fawn 10 mins The average would still be 30
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 17 Feb 2012, 21:35
kys123 wrote:
Statement 1 can't be correct because you don't know who out of the 2 is the faster drinker... John could drink faster than his friend or vice versa. Also you definition of average is wrong... Average mean A+B/2. A and B does not have to be the same. It could take John 50 mins to finish and Fawn 10 mins The average would still be 30


Faster drinker !!!! where does that come from???

St 1 Clearly states that "The average time it would take both to finish independently is 30 hours".

This clearly Implies : Rj = 1/30 , Rf= 1/30. In this case when they work together total time to finish this will be t=15.

But in the question they finish the work in 12 hrs. How come. The 1st statement is contradicting the question itself.

Are there any Gaps or am I misinterpreting.
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post Updated on: 18 Feb 2012, 02:57
GMATPASSION wrote:
kys123 wrote:
Statement 1 can't be correct because you don't know who out of the 2 is the faster drinker... John could drink faster than his friend or vice versa. Also you definition of average is wrong... Average mean A+B/2. A and B does not have to be the same. It could take John 50 mins to finish and Fawn 10 mins The average would still be 30


Faster drinker !!!! where does that come from???

St 1 Clearly states that "The average time it would take both to finish independently is 30 hours".

This clearly Implies : Rj = 1/30 , Rf= 1/30. In this case when they work together total time to finish this will be t=15.

But in the question they finish the work in 12 hrs. How come. The 1st statement is contradicting the question itself.

Are there any Gaps or am I misinterpreting.


Yes Mate. There is a big gap. How do you identify who is faster and who is slower. Given the information you cannot decide. The question is asking for an individual's time. Its the average time. Imagine the average time is \(30\) hrs for both of them. This could happen in so many ways. The two values could be \(20\) & \(40\) or the two values could be \(10\) & \(50\). More importantly, we wouldn't know who accounted for which. The average of both these scenarios would be \(30\), NO? An infinite number of possibilities exist with that "Average" information alone. Only Statement B tells us the "weight" of each contributor and tells us who was quicker. That alone should be enough information for you to pick B (along-with the fact that B limits to one variable alone), in most cases, unless it is another one of those GMAT trick questions :) However, this one clearly isn't and Statement B is hence enough. Since we know the relative weights of each contributor, B wins and is SUFFICIENT alone. I suggest you look up "Weighted Averages" on Wikipedia or some good Mathematics site. By the way Bunuel has composed an amazing Maths Book on the Gmat Club Forum and the more I read it, the more I realize how precise his understanding of the GMAT Quantitative section is. I seriously suggest you read it up. It will help clear a lot of tricky logic gaps. Hope I was able to explain it to you. And thanks Bunuel for pointing the error in my post.
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Originally posted by omerrauf on 18 Feb 2012, 00:50.
Last edited by omerrauf on 18 Feb 2012, 02:57, edited 5 times in total.
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 18 Feb 2012, 00:59
1
omerrauf wrote:
GMATPASSION wrote:
kys123 wrote:
Statement 1 can't be correct because you don't know who out of the 2 is the faster drinker... John could drink faster than his friend or vice versa. Also you definition of average is wrong... Average mean A+B/2. A and B does not have to be the same. It could take John 50 mins to finish and Fawn 10 mins The average would still be 30


Faster drinker !!!! where does that come from???

St 1 Clearly states that "The average time it would take both to finish independently is 30 hours".

This clearly Implies : Rj = 1/30 , Rf= 1/30. In this case when they work together total time to finish this will be t=15.

But in the question they finish the work in 12 hrs. How come. The 1st statement is contradicting the question itself.

Are there any Gaps or am I misinterpreting.


Yes Mate. There is a big gap. Its the average time. Imagine the average time is 30 hrs for both of them. This could happen in so many ways. The two values could be \(20\) & \(40\) or the two values could be \(10\) & \(50\). The average of both these scenarios would be \(30\), NO? An infinite number of possibilities exist with that "Average" information alone. Only Statement B tells us the "weight" of each contributor and that alone should be enough information for you to pick B, in most cases, unless it is another one of those GMAT trick questions :) However, this one clearly isn't and Statement B is hence enough. Since we know the relative weights of each contributor, B wins and is SUFFICIENT alone. Hope I was able to explain it to you.


Check the solution above: for (1) there exist only TWO combination of J and F, not more.
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 18 Feb 2012, 01:05
Yup. Right on Bunuel... My Bad....
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 18 Feb 2012, 04:12
Bunuel wrote:

But even though the formal answer to the question is B, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. In our question, from (2) we have that the average time is (30+20)/2=25 and (1) states that it's 30, so the statements clearly contradict each other.

In order it to be a realistic GMAT question (1) should read: The average time it would take John to finish the case drinking alone and Fawn to finish the case drinking alone is 25 hours. In this case for (1) we'll have: 1/J + 1/(50-J) = 1/12 --> J=30 (so F=20 --> J>F) or J=20 (so F=30 --> J<F). Statements don't contradict and (1) is still insufficient.

Hope it's clear.


Actually MGMAT flashcards did not provide the first statement. I made it up so that the whole question looks like a GMAT question. But I did not think of the point you mentioned. Great man :-D
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 27 Dec 2014, 12:16
Bunuel wrote:
Chembeti wrote:
John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

1) The average time it would take both to finish independently is 30 hours.
2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case.

This is actually from MGMAT flash cards. Looked interesting and hence I posted after modifying it a bit (I added a new statement).


John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

Given: 1/J + 1/F = 1/12

(1) The average time it would take both to finish independently is 30 hours --> J+F=60. Now, since we don't know which one drinks faster then even if we substitute F with 60-J (1/J + 1/(60-J) = 1/12) we must get two different answers for J and F: J<F and J>F. Not sufficient.

(2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case --> F=J-10 --> 1/J + 1/(J-10) = 1/12 --> J=4 (not a valid solution as F in this case is negative) and J=30 (F=20). Sufficient.

Now, technically the answer should be B, as Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

But even though the formal answer to the question is B, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. In our question, from (2) we have that the average time is (30+20)/2=25 and (1) states that it's 30, so the statements clearly contradict each other.

In order it to be a realistic GMAT question (1) should read: The average time it would take John to finish the case drinking alone and Fawn to finish the case drinking alone is 25 hours. In this case for (1) we'll have: 1/J + 1/(50-J) = 1/12 --> J=30 (so F=20 --> J>F) or J=20 (so F=30 --> J<F). Statements don't contradict and (1) is still insufficient.

Hope it's clear.



Hi Bunnel ,
(1) The average time it would take both to finish independently is 30 hours --> J+F=60. Now, if we substitute F with 60-J (1/J + 1/(60-J) = 1/12) we will get a quadratic in J with one +ive and one -ive Solution for J . Clearly J cannot be negative . so this statement should be sufficient . no ? Please advise , if i am missing something .

thanks
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 28 Dec 2014, 06:16
Lucky2783 wrote:
Bunuel wrote:
Chembeti wrote:
John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

1) The average time it would take both to finish independently is 30 hours.
2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case.

This is actually from MGMAT flash cards. Looked interesting and hence I posted after modifying it a bit (I added a new statement).


John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

Given: 1/J + 1/F = 1/12

(1) The average time it would take both to finish independently is 30 hours --> J+F=60. Now, since we don't know which one drinks faster then even if we substitute F with 60-J (1/J + 1/(60-J) = 1/12) we must get two different answers for J and F: J<F and J>F. Not sufficient.

(2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case --> F=J-10 --> 1/J + 1/(J-10) = 1/12 --> J=4 (not a valid solution as F in this case is negative) and J=30 (F=20). Sufficient.

Now, technically the answer should be B, as Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

But even though the formal answer to the question is B, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. In our question, from (2) we have that the average time is (30+20)/2=25 and (1) states that it's 30, so the statements clearly contradict each other.

In order it to be a realistic GMAT question (1) should read: The average time it would take John to finish the case drinking alone and Fawn to finish the case drinking alone is 25 hours. In this case for (1) we'll have: 1/J + 1/(50-J) = 1/12 --> J=30 (so F=20 --> J>F) or J=20 (so F=30 --> J<F). Statements don't contradict and (1) is still insufficient.

Hope it's clear.



Hi Bunnel ,
(1) The average time it would take both to finish independently is 30 hours --> J+F=60. Now, if we substitute F with 60-J (1/J + 1/(60-J) = 1/12) we will get a quadratic in J with one +ive and one -ive Solution for J . Clearly J cannot be negative . so this statement should be sufficient . no ? Please advise , if i am missing something .

thanks


Did you try to actually solve? You'd get two solutions for J, both positive: ~17 and ~43.
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Re: John and Fawn, each drinking at a constant pace, can finish  [#permalink]

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New post 10 Nov 2016, 00:45
Chembeti wrote:
John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

1) The average time it would take both to finish independently is 30 hours.
2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case.

This is actually from MGMAT flash cards. Looked interesting and hence I posted after modifying it a bit (I added a new statement).


Answer: Option B

Please check the solution as attached
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