GMAT Prep Question

[C Okigbo]

4. 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

[Brent@GMATPrepNow]

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.

Target question: How many of the animals are cows?

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

[OptimusPrep]

4. 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:
Total animals = 60. These will have cows, pigs, lions, giraffes, rabbits and so on.
Out of these, 40 are either pigs or cows.
Let us assume there are C cows and P pigs
So, C + P = 40

Question:
How many are cows.

Statement 1:
C > 2P
and we know C + P = 40
Let us try putting values of P here.
P = 10, C = 30
P = 11, C = 29
P = 12, C = 28
P = 13, C = 37
So we cannot get a definitive answer,
Hence statement 1 is not sufficient.

Statement 2:
P>12
There is not relation given between C and P here.
So we cannot say anything about the number of cows from this statement.
Be very careful not to take C > 2P from the statement 1 here.
This statement just gives us P > 12

Combining both 1 and 2:
C>2P and P>12
On substituing the values,
P = 13 and C = 27 (Satisfies both equations)
P = 14 and C = 26 (Does not satisfy both equations)

As we can see than only one set of values satisfy both the equations on combining them.
Hence C is the answer

[nikhilgmat31]

statement 1 says 2P < C
P+C = 40
C = 40-P
2P < 40 - P
3P < 40
p <40/3 NOT SUFFICIENT

Statement 2 says P > 12

combined 40/3>P>12 means P = 13 both together are SUFFICIENT.

Answer C