Q.Of the 60 animals on a certain farm,2/3 are either dogs or cats.How many of the animals are cats?
1.The farm has more than twice as many cats as it has dogs.
2.The farm has more than 12 dogs.
As per answer is a but OA is c.Please clarify.
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Pigs and cows = (2/3)(60) = 40.Of the 60 animals on a certain farm, 2/3 are either pigs or cows. 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
Question rephrased:
Of the 40 pig and cows, how many are cows?
Statement 1: The farm has more than twice as many cows as pigs
Case 1: pigs = 1 and cows = 39.
Case 2: pigs = 2 and cows = 38.
Since the number of cows can be different values, INSUFFICIENT.
Statement 2: The farm has more than 12 pigs
Case 3: pigs = 13 and cows = 27.
Case 4: pigs = 14 can cows = 26.
Since the number of cows can be different values, INSUFFICIENT.
Statements combined:
Both statements are satisfied only by Case 3:
pigs = 13 and cows = 27.
Thus, the number of cows = 27.
SUFFICIENT.
The correct answer is C.
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For some reason, your resource has changed the animals in the question, but everything else remains the same. Here's the ORIGINAL question.
Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows
Let P = # of pigs
Let C = # of cows
2/3 of 60 = 40, so we can say that P + C = 40
Statement 1: The farm has MORE THAN twice as many cows as it has pigs.
In other words, 2P < C
If we know 2P < C and P + C = 40, do we have sufficient information to find the value of C?
No. Consider these 2 conflicting cases:
Case a: P = 1 and C = 39, in which case there are 39 cows
Case b: P = 2 and C = 38, in which case there are 38 cows
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The farm has more than 12 pigs.
There's no way we can use this information to determine the number of cows.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 says that P > 12. So, let's examine some possibilities.
If P = 13, then C > 26 (from statement 1). So, C must equal 27 (since P + C = 40)
If P = 14, then C > 28 (from statement 1). In this case, P+C will be GREATER THAN 40, but we need P+C to EQUAL 40 (from the given information). So, P cannot equal 14.
In fact, for the same reasons, P cannot equal 15, 16, 17, etc. . .
So, the only case that's possible is for there to be 13 pigs and 27 cows
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Target question: How many of the animals are cows?Of the 60 animals on a certain farm, are either pigs or cows. How many of the animals are cows?
(1) The farm has more than twice as many cows as it has pigs.
(2) The farm has more than 12 pigs.
Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows
Let P = # of pigs
Let C = # of cows
2/3 of 60 = 40, so we can say that P + C = 40
Statement 1: The farm has MORE THAN twice as many cows as it has pigs.
In other words, 2P < C
If we know 2P < C and P + C = 40, do we have sufficient information to find the value of C?
No. Consider these 2 conflicting cases:
Case a: P = 1 and C = 39, in which case there are 39 cows
Case b: P = 2 and C = 38, in which case there are 38 cows
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The farm has more than 12 pigs.
There's no way we can use this information to determine the number of cows.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 says that P > 12. So, let's examine some possibilities.
If P = 13, then C > 26 (from statement 1). So, C must equal 27 (since P + C = 40)
If P = 14, then C > 28 (from statement 1). In this case, P+C will be GREATER THAN 40, but we need P+C to EQUAL 40 (from the given information). So, P cannot equal 14.
In fact, for the same reasons, P cannot equal 15, 16, 17, etc. . .
So, the only case that's possible is for there to be 13 pigs and 27 cows
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
