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Cows and pigs

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Cows and pigs

by sq720 » Sun May 03, 2009 5:44 am
Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows?

A.) the farm has more than twice as many cows as it has pigs
B.) the farm has more than 12 pigs.


C

I selected E because the second statment is saying that the farm has more than 12 pigs, so how could both statements be sufficient if we don't know the exact number of pigs
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by Objectivo » Sun May 03, 2009 5:50 am
Hi sq,

Since we know that the number of pigs + number of cows = 2/3s of 60, we know it's 40.

(1) tells us that that the number of cows is more than twice the number of pigs.

(2) tells us that there's more than 12 pigs. (which means at least 13)

So let's again look at the possiblities, taking into account that the solutions must be positive integers (since we're talking about animals)

If the number of pigs is 13, than the number of cows is at least 27, together they're (at least) 40. This is correct since the number of cows + the number of pigs was 40.

If the number of pigs is 14, than the number of cows is at least 28, but the sum of the two would be 42, which is greater than 40 and thus not possible (pigs + cows was 40)

Hence, (1) + (2) are sufficient, hence C is the anwer.
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Re: Cows and pigs

by Vemuri » Sun May 03, 2009 6:10 am
2/3 of the animals are either pigs or cows. So, # of cows or pigs in the farm = 40 (2/3*60)

Stmt1: This statement tells us that # of Cows >= 2 * # of Pigs. From this we cannot determine how many cows are in the farm. The # pigs might be 5 & the # of cows might be 35 or The # pigs might be 13 & the # of cows might be 27. Hence, this statement is not sufficient.

Stmt2: There are more than 12 pigs in the farm. We cannot determine how many cows are in the farm with just this much of information.

Combining both the statements, if pigs are more than 12, then they could be 13, 14, 15,..... If we use the condition in statement 1, then only 13 pigs will satisfy it. If there are 13 pigs, then there can be 27 cows (2*13=26. The condition states that cows are more than twice the number of pigs). If there are 14 pigs, then twice this number is 28 cows. Together, they are more than 40, which is not possible. Hence 13 pigs & 27 cows is the answer.

Hence C is the answer.
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