carcass wrote:
At the end of 2004, a certain farm had 24 hens, 12 cows, 30 sheep, and 14 pigs. By the end of 2005, 22 new animals — each either a hen, cow, sheep or pig — were brought to the farm. No animals left the farm. How many pigs were there on the farm at the end of 2005?
(1) The ratio of cows to pigs and the ratio of hens to sheep were the same at the end of 2004 and 2005.
(2) The number of sheep increased by 1/6 from the end of 2004 to the end of 2005
Statement 1:
H:S = 24:30 = 4:5.
In this ratio, the sum of the parts = 4+5 = 9.
Implication:
For the ratio to stay the same, H+S must increase by a multiple of 9.
C:P = 12:14 = 6:7.
In this ratio, the sum of the parts = 6+7 = 13.
Implication:
For the ratio to stay the same, C+P must increase by a multiple of 13.
Since the total number of animals increases by 22, only one case is possible:
H+S increases by 9 and C+P increases by 13, for a total increase of 22.
Since C+P increases by 13, there are 6 more cows and 7 more pigs.
Thus:
New pigs = 14+7 = 21.
SUFFICIENT.
Statement 2:
Increase in the number of sheep \(= \frac{1}{6}* 30 = 5\).
Since the total number of animals increases by 22, the increase in H+C+P = 22-5 = 17.
No way to determine the increase in P alone.
INSUFFICIENT.
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