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Of the 60 animals on a certain farm, 2/3 are either cows or
chini
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Of the 60 animals on a certain farm, 2/3 are either cows or pigs. How many of the animals are cows?

1) The farm has more than twice as many cows as pigs

2) The farm has more than 12 pigs

Answer is C, both statements together are sufficient.

Why isn't 1) alone sufficient? If there are at least twice as many cows as pigs, and there are either 40 pigs or 40 cows, then can't one conclude that the pigs must make up 2/3 of the total?
Re: Of the 60 animals on a certain farm, 2/3 are either cows
Ron Purewal
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chini wrote:
Of the 60 animals on a certain farm, 2/3 are either cows or pigs. How many of the animals are cows?

1) The farm has more than twice as many cows as pigs

2) The farm has more than 12 pigs

Answer is C, both statements together are sufficient.

Why isn't 1) alone sufficient? If there are at least twice as many cows as pigs, and there are either 40 pigs or 40 cows, then can't one conclude that the pigs must make up 2/3 of the total?


unfortunately, you're misinterpreting the problem statement.

the statement "2/3 are either cows or pigs" doesn't mean that there are either 40 cows or 40 pigs. it means that, if you take the cows and the pigs together, they constitute 2/3 of the animals on the farm.
in other words, cows + pigs = 40.
(i can understand your alternate reading of the problem statement; it's reasonable enough. just remember that the gmat is their playground, not yours, and so you have to play by their rules - so remember the way certain statements are written. as a postscript, i hope that future problems like this one will be purged and/or rewritten for clarity before they make it into the official question pool; it would be a shame if students miss the problem just because of its ambiguity.)

thus:

(1)
this means that there are at least 27 cows (because 27 cows, 13 pigs is the least # of cows satisfying this criterion).
that's all we know, though; there could be anywhere between 27 cows (and therefore 13 pigs) and 40 cows (and therefore 0 pigs).
insufficient

(2)
this means that there are at least 13 pigs, which means that there are at most 27 cows.
that's all we know.
insufficient

(together)
(1) says there are at least 27 cows; (2) says there are at most 27 cows.
so, there are 27 cows and 13 pigs.
sufficient

answer = c
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Thank you very much, Ron!
Rey Fernandez
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We're glad it helped!
Amit
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@Ron,
From (1) can't we have 28 Cows and 12 pigs as well.

"his means that there are at least 27 cows (because 27 cows, 13 pigs is the least # of cows satisfying this criterion). "

Am I missing something here.

Amit
Ron Purewal
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Amit wrote:
@Ron,
From (1) can't we have 28 Cows and 12 pigs as well.

"his means that there are at least 27 cows (because 27 cows, 13 pigs is the least # of cows satisfying this criterion). "

Am I missing something here.

Amit


no, you're right - but go back and read the original post again. under statement (1), i wrote that you can have any possibility of (cows, pigs) between (27, 13) and (40, 0).
this means you could have (27, 13), (28, 12), (29, 11), ..., (40, 0).
that's why the statement is insufficient.
Of the 60 animals on a certain farm, 2/3 are either cows or
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