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Horses

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by N:Dure » Wed Dec 01, 2010 10:23 am
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Source: — Problem Solving |

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by Rahul@gurome » Wed Dec 01, 2010 11:05 am
Say, number of horses = H and number of ponies = P and H = (P + 3).

To minimize the number of horses and ponies we have to minimize both H and P. As H = (P + 3), minimizing P also minimizes H. Thus the problem boils down to minimization of P.

Number of ponies with horseshoe = 5P/6
5P/6 must be an integer => P must be a multiple of 6.

Number of Icelandic ponies = (2/3)*(Number of ponies with horseshoe) = (2/3)*(5P/6) = 5P/9
5P/9 must be an integer => P must be a multiple of 9.

Minimum possible value of P such that P is multiple of 6 and 9 is 18.
=> Minimum possible value of H = (18 + 3) = 21

Minimum number of horses and ponies combined in that ranch = (18 + 21) = 39

The correct answer is D.
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by Laura GMAT Tutor » Wed Dec 01, 2010 11:34 am
Ah, while I was drawing a picture to explain this one, Rahul wrote a pretty nice explanation :)

Well, maybe you guys will still like the visual aid. I always use flowcharts to organize questions with "this fraction of this is then broken down into that fraction of that..." setups.

hope it's helpful.
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by trangle » Wed Dec 01, 2010 3:38 pm
The smallest number we can pick in this problem for ponies is 18 since 18 is divided evenly by 6 in order to have 15 as number of horseshoed ponies, and 15 divided evenly by 3 to have 10 Icelandic ponies (6 or 12 will not work).

If there are 18 ponies at the ranch, so there are 15 (5/6 of 18) ponies that have horseshoes, and there are 10 (2/3 of 25) are Icelandic.

If there are three horses more than ponies, there will be 21 horses. The minimum number of horses and ponies combined in the ranch will be 21+18=39.

What do you think about my approach?
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