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04 May 2020, 10:52
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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).
Class Assignment
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).
----------
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).
Class Assignment
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04 May 2020, 11:21
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Please go through this topic before posting questions.
https://gmatclub.com/forum/rules-for-po ... 33935.html.
Bunuel san, I think there are 5-6 questions like this. Can you delete or move them?
https://gmatclub.com/forum/rules-for-po ... 33935.html.
Bunuel san, I think there are 5-6 questions like this. Can you delete or move them?
04 May 2020, 11:24
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ahmadali0
This question is discussed here: a-ranch-has-both-horses-and-ponies-exactly-5-6-of-the-132328.html Please go through that discussion and in case of any doubts please post there. Hope it helps.
THIS TOPIC IS LOCKED AND ARCHIVED.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
