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17 Feb 2012, 19:53
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
54% (02:04) correct
46%
(02:22)
wrong
based on 843
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Not Attempted Yet
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).
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).
17 Feb 2012, 21:55
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Chembeti
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).
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.
General Discussion
boomtangboy
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17 Feb 2012, 21:11
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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
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
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. 
