Data Sufficiency

OA: C

Please explain..

First, we know that pigs and cows together total 40. (2/3 of 60)

Statement 1 tells us there are more than twice as many cows as pigs. We could have 39 cows and 1 pig or 38 cows and 2 pigs, etc. Insufficient.

Statement 2 tells us there are more than 12 pigs. We could have 20 pigs and 20 cows or 15 pigs and 25 cows, etc. Insufficient.

Putting them together, from the second statement we know there are more than 12 pigs; we have to have at least 13.
Combining that with the first statement, if there are 13 pigs there are more than 26 cows. That would give us at least 27 cows and 13 pigs - total 40. That works. If we had 14 pigs, we would have at least 29 cows - total 43 - too many. Therefore the only value that works is 13 pigs.

The question gives c + p = (3/4)*60 = 40.

p = ?

Statement 1) c > 2p, and c + p = 40 from question stem

Since 2p < c, 2p + p = 3p < 40, so p < 40/3 = 13.333. 0 <= p <= 13, and 40-13 = 27 <= c <= 40.

c and p could take on many values within these constraints, so the statement is insufficient.

Statement 2) even with p > 12, p and c have many possible values that add to 40, such as (40,0), (39,1), (14,26), etc. Insufficient.

Combined) 0 <= p <= 13 and p > 12, so 12 < p <= 13, and p must equal the integer 13. Sufficient.

C

thnaks both of you