A ranch has horses and ponies. Five-sixths of the ponies have horsesho

Question

A ranch has horses and ponies. Five-sixths of the ponies have horseshoes. Half of the ponies with horseshoes are Icelandic. If there are three more horses than ponies, what is the minimum number of horses and ponies on the ranch?

A. 12
B. 15
C. 27
D. 48
E. 54

A. 12
B. 15
C. 27
D. 48
E. 54

Archit3110 · Answer

given
H=3+P

so let h+p = 27
or say 
2p+3=27
p=12 and horses ; 15 
so Five-sixths of the ponies have horseshoes ; 10 
and Half of the ponies with horseshoes are Icelandic ; 5
If there are three more horses than ponies ; 15
IMO C ; 27 sufficient

eakabuah · Answer

From the question stem we know that 5/6 ponies (p) have horseshoes. In addition we know that half of the ponies with with horseshoe are Icelandic. And there are three more horses than ponies. We are to find the minimum number of ponies and horses on the ranch.

Icelandic p=(5/12)p
The minimum value of p which makes the number of ponies which are Icelandic = 5p/12 equal to an integer, in this case 5 is the minimum number of ponies.
This implies that p=12 is the minimum possible number of ponies on the ranch.
Total number of ponies and horses =12+(12+3)=27.

The answer is therefore C.

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vinayakvaish · Answer

let ponies be p
horses are then p+3
total= 2p+3

5/6*1/2*p= some type of ponies that is an integer
5/12*p is an integer hence p is divisible by 12

The minimum value of P can be 12

total= 2*12+3= 27

Answer C

Kinshook · Answer

Minimum number of ponies =12
Minimum number of horses=12+3=15
Minimum number of horses and ponies = 12+15=27

IMO C

Posted from my mobile device

Mykonos · Answer

I understand the solutions posted, but doesn't the pair of 9 horses and 6 ponies satisfy the min? There are 3 more horses than ponnies, and you can have 5 ponies with horseshoes (5/6*6) while half of them (6/2=3) would be Icelandic. What am I missing here?

adewale223 · Answer

Let number of ponies be x.

Number of horse shoe ponies = 5x/6

Half of horseshoe are icelandic

5x/12

Now number of ponies has to be an integer so lowest multiple of 6 and 12 = 12.

Then number of horses will be 15.

Total minimum number

12+15 = 27.

Posted from my mobile device

ScottTargetTestPrep · Answer

We can let the number of ponies = p

Thus, 5p/6 = horseshoes

1/2 * 5p/6 = 5p/12 = Icelandic

Thus, the minimum number of ponies is 12, and since there are 3 more horses than ponies, the minimum number of horses is 15. Thus, the minimum total is 27.

Answer: C

bumpbot · Answer

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A ranch has horses and ponies. Five-sixths of the ponies have horsesho

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