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Milkman

by harsh.champ » Mon Feb 08, 2010 4:49 am
A milkman has 25 small cans, all of which are completely filled with milk. He also has one large can
which is empty. Can he transfer all the milk contained in 15 of these small cans to the large can?
A: The large can has a capacity of 500 liters.
B: The average capacity of any 20 of the small cans is 25 liters.

The OA is D.
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by shashank.ism » Mon Feb 08, 2010 4:50 am
harsh.champ wrote:A milkman has 25 small cans, all of which are completely filled with milk. He also has one large can
which is empty. Can he transfer all the milk contained in 15 of these small cans to the large can?
A: The large can has a capacity of 500 liters.
B: The average capacity of any 20 of the small cans is 25 liters.

The OA is D.
A insufficient don't know the vol of small cans
B insufficient don't know about others small cans and even the large one.
combined insufficient : vol of large one is known and 1 small can is known but not other small cans,,,

Ans D
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by stufigol » Mon Feb 08, 2010 3:17 pm
ans=E
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by jeffedwards » Mon Feb 08, 2010 5:08 pm
C
Statement A: Insufficient, don't know the size of the 15 small cans
Statement B: Insufficient, don't know the size of the container
Together: Sufficient, we know that the average of 20 of the small cans is 25 liters, so the 15 small cans have to be ≤ 25 (15 is included in the small cans and the rest would either be ≥ to the small cans). Since 15*25 is 375 liters, we know that all of the small cans can be transferred into the large can, since 375 is the largest maximum volume

Why are people saying D (Either); shouldn't it be C (Together)?
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by Stuart@KaplanGMAT » Mon Feb 08, 2010 6:03 pm
harsh.champ wrote:A milkman has 25 small cans, all of which are completely filled with milk. He also has one large can
which is empty. Can he transfer all the milk contained in 15 of these small cans to the large can?

1: The large can has a capacity of 500 liters.
2: The average capacity of any 20 of the small cans is 25 liters.

The OA is D.
It's clear that neither statement is sufficient by itself - there's no way the answer is D.

Together we can answer the question.

The key word in statement (2) is "any".

Since "any of the 20 small cans" have an average capacity of 25l, that means that each can must have a 25l capacity (if some had different capacities, then choosing different sets of 20 cans would yield different averages).

So, combined we know the exact capacity of both the large and small cans; accordingly, we can answer the question.

Choose C.
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by harsh.champ » Mon Feb 08, 2010 11:51 pm
Stuart Kovinsky wrote:
harsh.champ wrote:A milkman has 25 small cans, all of which are completely filled with milk. He also has one large can
which is empty. Can he transfer all the milk contained in 15 of these small cans to the large can?

1: The large can has a capacity of 500 liters.
2: The average capacity of any 20 of the small cans is 25 liters.

The OA is D.
It's clear that neither statement is sufficient by itself - there's no way the answer is D.

Together we can answer the question.

The key word in statement (2) is "any".

Since "any of the 20 small cans" have an average capacity of 25l, that means that each can must have a 25l capacity (if some had different capacities, then choosing different sets of 20 cans would yield different averages).

So, combined we know the exact capacity of both the large and small cans; accordingly, we can answer the question.

Choose C.
Sorry to say ,
But I just made a typo error in the OA in the original question above.
The OA will be C not D.
Thanks for pointing it out Stuart.

Only,when we combine both the statements do we get the exact capacity of both the cans and thus we will get the answer.
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by sanju09 » Tue Feb 09, 2010 12:27 am
harsh.champ wrote:A milkman has 25 small cans, all of which are completely filled with milk. He also has one large can
which is empty. Can he transfer all the milk contained in 15 of these small cans to the large can?
A: The large can has a capacity of 500 liters.
B: The average capacity of any 20 of the small cans is 25 liters.

The OA is D.
We have the freedom of taking the capacity of each of the small can to be v, and that of the large can to be V to answer: Is 15 v ≤ V?

(1) With V = 500 liter we cannot answer "Is 15 v ≤ V?" Insufficient

(2) This allows us to live in the same freedom that each small can is of same capacity, v for us, and there's more that v = 25 liter. But, we still cannot answer "Is 15 v ≤ V?" with that piece of info only. Insufficient

Taken together

With v and V known, "Is 15 v ≤ V?" can be unmistakably answered. Sufficient

[spoiler]C[/spoiler]
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