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pigs and cows in a farm

Expert replies
by Amrabdelnaby » Fri Jan 01, 2016 7:06 am
Of the 60 animals in the farm, 2/3 of the animals are either cows or pigs. How many of the animals are cows?

1) the farm has more than twice as many cows as it has big

2) the farm has more than 12 pigs

Pls explain
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Source: — Problem Solving |

by DavidG@VeritasPrep » Fri Jan 01, 2016 7:16 am
Amrabdelnaby wrote:Of the 60 animals in the farm, 2/3 of the animals are either cows or pigs. 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

Pls explain
If 2/3 of the 60 animals are cows or pigs, then 60 * (2/3) = 40 are cows or pigs. So Cows + Pigs = 40.

Statement 1:There could be 39 cows and 1 pig or 38 cows and 2 pigs, etc. Not sufficient.

Statement 2: there could be 13 pigs and 27 cows, there could be 14 pigs and 26 cows, etc. Not sufficient.

Together. We've got three pieces: 1) cows and pigs sum to 40; 2)there are more than twice as many cows as pigs; 3) there are more than 12 pigs
The only scenario that will satisfy all three: 27 cows and 13 pigs. (If there were 26 cows and 14 pigs, there wouldn't be more than twice as many cows. If there were 28 cows and 12 pigs, there wouldn't be more than 12 pigs.) Because there is a unique value - 27 cows - together the statements are sufficient. Answer is C
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by Brent@GMATPrepNow » Fri Jan 01, 2016 10:52 am
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.
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
Last edited by Brent@GMATPrepNow on Mon Jan 25, 2016 10:43 am, edited 1 time in total.
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by jain2016 » Mon Jan 25, 2016 9:23 am
2/3 of 60 = 40, so we can say that P + C = 40

Hi Brent ,

Just a quick question. why can we say that P+c=40?

We have only given either P = 2/3*60 or C=2/3*60 right?

Please explain and correct me if took in other way.

Many thanks in advance.

SJ
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by Brent@GMATPrepNow » Mon Jan 25, 2016 10:46 am
jain2016 wrote:
2/3 of 60 = 40, so we can say that P + C = 40

Hi Brent ,

Just a quick question. why can we say that P+c=40?

We have only given either P = 2/3*60 or C=2/3*60 right?

Please explain and correct me if took in other way.

Many thanks in advance.

SJ
If P = # of pigs and C = # of cows, then P + C = total number of pigs and cows.
Since 40 of the animals (2/3 of 60) are either pigs or cows, we can conclude that P + C = 40

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by regor60 » Mon Jan 25, 2016 11:27 am
jain2016 wrote: We have only given either P = 2/3*60 or C=2/3*60 right?

SJ
No. That would be written "either the cows or the pigs are 2/3"

The intention of the wording is that a group of 40 animals (2/3x60) is made up of both cows and pigs
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by jain2016 » Mon Jan 25, 2016 10:12 pm
Brent@GMATPrepNow wrote:
jain2016 wrote:
2/3 of 60 = 40, so we can say that P + C = 40

Hi Brent ,

Just a quick question. why can we say that P+c=40?

We have only given either P = 2/3*60 or C=2/3*60 right?

Please explain and correct me if took in other way.

Many thanks in advance.

SJ
If P = # of pigs and C = # of cows, then P + C = total number of pigs and cows.
Since 40 of the animals (2/3 of 60) are either pigs or cows, we can conclude that P + C = 40

Cheers,
Brent
Hi Brent,

Thanks for your reply.

So what I understood is that, here, "either the cows or the pigs are 2/3" means P+C=40 right?

Please advise.

Thanks,

SJ
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