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25 Aug 2020, 20:00
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Difficulty:
85%
(hard)
Question Stats:
58% (02:50) correct
42%
(03:06)
wrong
based on 561
sessions
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On Sunday, in Alexa’s stable, the ratio of the number of ponies to the number of horses was 4:5. On Monday, she bought 35 more ponies and horses, then the ratio of ponies to horses became 5:8. Assuming that no animal left the stable or died and stable had ponies and horses only, what is the least number of horses that were there in the stable on Sunday?
A. 35
B. 55
C. 60
D. 65
E. 70
A. 35
B. 55
C. 60
D. 65
E. 70
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25 Aug 2020, 20:26
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On Sunday, in Alexa’s stable, the ratio of the number of ponies to the number of horses was 4:5. On Monday, she bought 35 more ponies and horses, then the ratio of ponies to horses became 5:8. Assuming that no animal left the stable or died and stable had ponies and horses only, what is the least number of horses that were there in the stable on Sunday?
A. 35
B. 55
C. 60--> correct
D. 65
E. 70
Solution:
# of pony & #of horse
Sun: 4x & 5x
Monday bought: # of ponies = 35-h & # of horses =h
# of pony & #of horse
Total on Monday: 4x+35-h & 5x+h
So \(\frac{4x+35-h}{5x+h} = \frac{5}{8}\)
=> 32x+280-8h=25x+5h
=> 7x+280=13h
=> \(h =\frac{7x+280}{13} =\frac{7x+ (21*13+7)}{13} =\frac{7(x+ 1)}{13} + 21 \) --> # of horses, h is a positive integer so x+1 has to be multiple of 13
=> x+1=13d, where d =1,2,3,
# horses on sunday=5x
=> 5x=5(13d-1), min(d)=1
=> 5x= 5*12=60
Answer: C
A. 35
B. 55
C. 60--> correct
D. 65
E. 70
Solution:
# of pony & #of horse
Sun: 4x & 5x
Monday bought: # of ponies = 35-h & # of horses =h
# of pony & #of horse
Total on Monday: 4x+35-h & 5x+h
So \(\frac{4x+35-h}{5x+h} = \frac{5}{8}\)
=> 32x+280-8h=25x+5h
=> 7x+280=13h
=> \(h =\frac{7x+280}{13} =\frac{7x+ (21*13+7)}{13} =\frac{7(x+ 1)}{13} + 21 \) --> # of horses, h is a positive integer so x+1 has to be multiple of 13
=> x+1=13d, where d =1,2,3,
# horses on sunday=5x
=> 5x=5(13d-1), min(d)=1
=> 5x= 5*12=60
Answer: C
25 Aug 2020, 20:32
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Sunday -- Ponies: Horses = 4:5.
On Monday, 35 new animals were added (can be ponies, can be horses) and the new ratio Ponies:Horses = 5:8
5:8 = 5+8 = 13. We need the total number of horses on Monday to be a multiple of 13.
I tried reverse calculating using the answer choices.
1. 35 horses on Sunday. Ponies on Sunday = 28. Total = 63. After adding 35 to this, gives us 98, which is not a multiple of 13.
2. Horses = 55. Ponies = 44. Total = 99. Plus 35 = 134. Wrong
3. Horses = 60. Ponies = 48. Total = 108. Plus 35 = 143. which is a multiple of 13.
Correct answer: C : 60.
On Monday, 35 new animals were added (can be ponies, can be horses) and the new ratio Ponies:Horses = 5:8
5:8 = 5+8 = 13. We need the total number of horses on Monday to be a multiple of 13.
I tried reverse calculating using the answer choices.
1. 35 horses on Sunday. Ponies on Sunday = 28. Total = 63. After adding 35 to this, gives us 98, which is not a multiple of 13.
2. Horses = 55. Ponies = 44. Total = 99. Plus 35 = 134. Wrong
3. Horses = 60. Ponies = 48. Total = 108. Plus 35 = 143. which is a multiple of 13.
Correct answer: C : 60.
