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 Post subject: GMAT Fractions
PostPosted: Sun Mar 20, 2011 1:22 pm 
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A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?

A. 18
B. 21
C. 38
D. 39
E. 57

(D) The trick to this question is that the number of Icelandic ponies cannot be fractional. It must be an integer.
The number of Icelandic ponies is:
(2/3) × (5/6) × total number of ponies, or
10/18 × total number of ponies.

9 is the smallest positive integer that yields another integer when multiplied by 5/9, and all multiples of 9 will yield a whole number of Icelandic ponies.

However, the number of ponies must also be a multiple of 6 so that the number of ponies with horseshoes is an integer. If there were only 9 ponies, the number of ponies with horseshoes would be:
(5/6) × 9 = 15/2. This is impossible.

The least common multiple of 6 and 9 is 18, so there are 18 ponies at minimum.

If there are 18 ponies, then there must be 18 + 3 = 21 horses. Since 18 + 21 = 39, the minimum number of horses and ponies on the ranch is 39.

The correct answer is choice (D).
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The answer can also be 21 (12+9). i.e. 12 horses and 9 ponies. if there are 9 ponies,the total no.of iceland ponies will be 10/18 x 9 = 5 ponies. So combined no. of animals shall be 21(minimum).


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 Post subject: Re: math (t.1, qt. 16): fractions
PostPosted: Sun Mar 20, 2011 1:33 pm 
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If there were 9 ponies, then the number of the ponies with horseshoes would be 9 × 5/6 = 15/5 = 7.5. That is the fractional value and can NOT be true.

The key to solve this problem is to keep in mind that all the values must NOT be fractional: the number of the ponies with horseshoes and the number of the ponies with horseshoes from Iceland.


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 Post subject: Re: math (t.1, qt. 16): fractions
PostPosted: Wed May 23, 2012 4:46 am 
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Could you please explain this question more in detail?

Thank You


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 Post subject: Re: math (t.1, qt. 16): fractions
PostPosted: Wed May 23, 2012 5:01 am 
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 Post subject: Re: math (t.1, qt. 16): fractions
PostPosted: Sun Jun 10, 2012 5:22 pm 
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It is a very good question indeed.


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 Post subject: Re: GMAT Fractions
PostPosted: Thu Sep 13, 2012 4:23 am 
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Can the answer be B?


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 Post subject: Re: GMAT Fractions
PostPosted: Thu Sep 13, 2012 4:30 am 
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 Post subject: Re: GMAT Fractions
PostPosted: Wed Apr 17, 2013 4:44 pm 
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Is this problem missing a qualifier for the ponies? It seems the info about shoes and Iceland are irrelevant. It's only asking for horses and ponies combined, right? I would think the solution would be Total = subtract 3 and divide by two. B creates the smallest whole number. What am I missing on this question? Thanks


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 Post subject: Re: GMAT Fractions
PostPosted: Wed Apr 17, 2013 4:44 pm 
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