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

Thank you very much, Ron!

We're glad it helped!

@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.

1. pigs + cows = 2/3 of 60 = 40
thus, p+c = 40

stmt1:
cows are more than twice the number of pigs.
=> c> 2p
therefore p+c = 40
=> p + 2p < 40 since c> 2p
=> p< 40/3
=> p< 13.333
since number of pigs can't be a fraction, the various values for p
can be 13,12,11 and so on..
correspondingly cows can be 27, 28 .. and so on..
there is no unique value . So stmt1 is insufficient

stmt2: p > 12
=> p can be 13,14,15, and so on
correspondingly cows can be 27, 26 and so on..
there is no unique value for the number of cows, thus stmt2 is insufficient

stmt1 and stmt2 :
p>12 and p< 13.333
=> p =13 because number of pigs must be an integer and not a fraction

Thus, p=13 implies ,number of cows =27

Therefore answer is (C)

That right. And thorough.

And it so happened that I got the same problem on the GMATPrep test that I took a couple of hours ago....

And it so happened that I interpreted the question in the same way as chini did ...
And it so happened that I chose the same answer i.e, A :( ...

I know the old adage: Do not question the official problems and explanation" but shouldn't the question say "2/3 are pigs and cows" rather than "2/3 are either pigs or cows".

No. How can they be both pigs and cows? Question says 2/3 are (that means, 40 of them are) either pigs or cows. In other words, out of 60, 40 of them are either pigs or cows. The usage is correct.

Exactly!

_________________
Jamie Nelson
ManhattanGMAT Instructor

Sorry Ron, could you please explain what was the ambiguity in this question? I thought it is clear, no? Thanks.

if you thought it was clear, then, good! in that case, you don't *want* to think about the potential ambiguity -- why create confusion out of clarity?

the original poster had interpreted the statement as "either 2/3 cows or 2/3 pigs".

Ahh cool. Although it does not make sense, but somebody can definitely interpret it that way - SC overload.

Now that I think, if it were an SC question, what could be the right usage? I can't find a concise way to make it absolutely clear. Any suggestions? Sorry to take this topic in a bit different direction, but it would be enlightening to understand the right usage.

May be: There are 60 animals on a certain farm; of the 2/3 of these animals, some are cows and others are pigs. If this is correct, do you think we need a COMMA after cows?

Thanks so much :)

hi -- this is a verbal question, so please make a new thread in the general verbal folder. it's important that we stay on topic within each folder.
thanks.