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 twice as many cows as it has pigs.
2) The farm has more than 12 pigs
B
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Pigs or cows
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Brent@GMATPrepNow
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IMPORTANT: You incorrectly transcribed the question. It SHOULD read as follows . . .
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?josh80 wrote: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 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
Last edited by Brent@GMATPrepNow on Sat Mar 01, 2014 1:21 pm, edited 2 times in total.
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Quick note: as written, (1) is both sufficient and impossible. Brent corrected the statement in his explanation.josh80 wrote: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 twice as many cows as it has pigs.
2) The farm has more than 12 pigs
B
(I say (1) is impossible because it would require the farm to have (2/3)(40) = 26 2/3 cows, which is both messy and illegal in some states.)
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mariofelixpasku
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why isnt it 2P < C ?
Brent@GMATPrepNow wrote:Question edited below . . .
Target question: How many of the animals are cows?josh80 wrote: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 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, P < 2C
If we know P < 2C 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
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Brent@GMATPrepNow
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You're absolutely right - Good catch, thanks!mariofelixpasku wrote:why isn't it 2P < C ?
I've edited my response accordingly.
Cheers,
Brent
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Jeff@TargetTestPrep
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We are given that of the 60 animals on a certain farm, 2/3 are either pigs or cows.josh80 wrote: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 twice as many cows as it has pigs.
2) The farm has more than 12 pigs
If we let c = the number of cows and p = the number of pigs, we can create the following equation:
c + p = 2/3(60)
c + p = 40
We must determine the value of c.
Statement One Alone:
The farm has more than twice as many cows as it has pigs.
Using the information in statement one, we can create the following inequality:
c > 2p
We also can isolate p in our original given equation of c + p = 40.
p = 40 - c
Since p = c - 40, we can substitute c - 40 for p in the inequality c > 2p.
c > 2(40 - c)
c > 80 - 2c
3c > 80
c > 80/3
c > 26 2/3
We still cannot determine the number of cows. Statement one is not sufficient to answer the question.
Statement Two Alone:
The farm has more than 12 pigs.
Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
From statements one and two, we know that c > 26 2/3 and that p > 12. From the given information, we know that c + p = 40. Based on our inequalities, the only possible values of c and p that sum to 40 are 27 and 13, respectively. Thus, there are 27 cows on the farm.
Answer: C
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Target question: How many of the animals are cows?josh80 wrote: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 twice as many cows as it has pigs.
2) The farm has more than 12 pigs
B
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
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Brent@GMATPrepNow
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Target question: How many of the animals are cows?josh80 wrote: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 twice as many cows as it has pigs.
2) The farm has more than 12 pigs
B
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
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