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.
Horses
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Rahul@gurome
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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.
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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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?
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?
