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).
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.