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in Danny’s farmhouse

by sanju09 » Thu Feb 09, 2012 4:15 am
There are a total of 35 all healthy pets that include cows, dogs, goats, and as many hens as the number of dogs and goats put together in Danny's farmhouse. How many cows are there in Danny's farmhouse?
I. The total number of legs of all pets in Danny's farmhouse count 116.
II. The total number of horns of all pets in Danny's farmhouse count 32.



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by Brent@GMATPrepNow » Thu Feb 09, 2012 9:14 am
sanju09 wrote:There are a total of 35 all healthy pets that include cows, dogs, goats, and as many hens as the number of dogs and goats put together in Danny's farmhouse. How many cows are there in Danny's farmhouse?
I. The total number of legs of all pets in Danny's farmhouse count 116.
II. The total number of horns of all pets in Danny's farmhouse count 32.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
Hi Sanjeev,

I think the assumption here is that cows have 2 horns each (if they don't have horns, then we get 2 contradicting statements). According to various, possibly unreliable sources, some cows have horns, and some don't. That said, let's go on the following assumptions (because I'd hate to see such a great question go to waste):
- cows have 2 horns and 4 legs
- dogs have 0 horns and 4 legs
- goats have 2 horns and 4 legs
- hens have 0 horns and 2 legs

Let C = # of cows, D = # of dogs, G = # of goats, and H = # of hens

Given info:
- 35 all healthy pets: C+D+G+H=35
- As many hens as the number of dogs and goats put together: H=D+G

If we replace H with D+G, we get: C+D+G+(D+G)=35
Simplify to get: C+2D+2G=35

Target question: What is the value of C?

Statement 1: The total number of legs of all pets in Danny's farmhouse count 116.
We can write: 4C+4D+4G+2H=116
Replace H with D+G to get: 4C+4D+4G+2(D+G)=116
Simplify to get: 4C+6D+6G=116
Can we determine the value of C?
Yes.
Take C+2D+2G=35 and multiply both sides by 3 to get: 3C+6D+6G=105
Now subtract this equation (3C+6D+6G=105) from 4C+6D+6G=116 to get: C=11
Since we can definitively answer the target question, statement 1 is SUFFICIENT

Statement 2: The total number of horns of all pets in Danny's farmhouse count 32.
2C+2G=32
Divide both sides by 2 to get: C+G=16
So, we have two equations to work with: C+G=16 and C+2D+2G=35
Can we determine the value of C?
No.
We can see the problem if we rewrite C+2D+2G=35 as C+G+G+2D=35
Now replace C+G with 16 to get: 16+G+2D=35
Simplify to get: G+2D=16
There are several possible values for C here, so statement 2 is INSUFFICIENT

So, the answer is A.

Cheers,
Brent
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by sanju09 » Fri Feb 10, 2012 5:11 am
Brent@GMATPrepNow wrote:
sanju09 wrote:There are a total of 35 all healthy pets that include cows, dogs, goats, and as many hens as the number of dogs and goats put together in Danny's farmhouse. How many cows are there in Danny's farmhouse?
I. The total number of legs of all pets in Danny's farmhouse count 116.
II. The total number of horns of all pets in Danny's farmhouse count 32.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
Hi Sanjeev,

I think the assumption here is that cows have 2 horns each (if they don't have horns, then we get 2 contradicting statements). According to various, possibly unreliable sources, some cows have horns, and some don't. That said, let's go on the following assumptions (because I'd hate to see such a great question go to waste):
- cows have 2 horns and 4 legs
- dogs have 0 horns and 4 legs
- goats have 2 horns and 4 legs
- hens have 0 horns and 2 legs

Let C = # of cows, D = # of dogs, G = # of goats, and H = # of hens

Given info:
- 35 all healthy pets: C+D+G+H=35
- As many hens as the number of dogs and goats put together: H=D+G

If we replace H with D+G, we get: C+D+G+(D+G)=35
Simplify to get: C+2D+2G=35

Target question: What is the value of C?

Statement 1: The total number of legs of all pets in Danny's farmhouse count 116.
We can write: 4C+4D+4G+2H=116
Replace H with D+G to get: 4C+4D+4G+2(D+G)=116
Simplify to get: 4C+6D+6G=116
Can we determine the value of C?
Yes.
Take C+2D+2G=35 and multiply both sides by 3 to get: 3C+6D+6G=105
Now subtract this equation (3C+6D+6G=105) from 4C+6D+6G=116 to get: C=11
Since we can definitively answer the target question, statement 1 is SUFFICIENT

Statement 2: The total number of horns of all pets in Danny's farmhouse count 32.
2C+2G=32
Divide both sides by 2 to get: C+G=16
So, we have two equations to work with: C+G=16 and C+2D+2G=35
Can we determine the value of C?
No.
We can see the problem if we rewrite C+2D+2G=35 as C+G+G+2D=35
Now replace C+G with 16 to get: 16+G+2D=35
Simplify to get: G+2D=16
There are several possible values for C here, so statement 2 is INSUFFICIENT

So, the answer is A.

Cheers,
Brent
Hi Brent,

Thanks for identifying the loop hole. I now believe there is some assumption with the healthy cows the question is talking about, and I am still clueless if the same assumption goes with the healthy goats as well. I have just seen the following Wiki link in curiosity

https://wiki.answers.com/Q/Do_cows_have_horns

Thanks for answering.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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