HOT Competition: On Sunday, in Alexa’s stable, the ratio of the number

Question

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

This question was provided by GMATWhiz
for the Heroes of Timers Competition

Show Answer

Official Answer

C

A. 35
B. 55
C. 60
D. 65
E. 70

hiranmay · Accepted Answer

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

This question was provided by GMATWhiz
for the Heroes of Timers Competition

Show Answer

Official 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

aviddd · Answer

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.

BenjaminS · Answer

Let me explain.

On Sunday, the ratio of p (the number of ponies) to h (the number of horses) was 4:5.
On Monday, Add 35 more ponies and horses. Then, the ratio of the number of ponies to the number of horses was 5:8.

So I test the choice
A: the number of horses on Sunday = 35 
On Sunday, the ratio p to h = 28/35
On Monday, the ration p to h can be 30/48
 Therefore, the additional p and h = 2+13 = 15 
 On Monday, the ration p to h can be 35/56
 Therefore, the additional p and h = 7+21 = 28 
 On Monday, the ration p to h can be 40/64
 Therefore, the additional p and h = 12+29 = 41 
 Out.

B: the number of horses on Sunday = 55 
On Sunday, the ratio p to h = 44/55
On Monday, the ration p to h can be 45/72
 Therefore, the additional p and h = 1+17 = 18 
On Monday, the ration p to h can be 50/80
 Therefore, the additional p and h = 6+25 = 31 
On Monday, the ration p to h can be 55/88
 Therefore, the additional p and h = 11+33 = 44 
 Out

C: the number of horses on Sunday = 60
On Sunday, the ratio p to h = 48/60
On Monday, the ration p to h can be 55/88
  Therefore, the additional p and h = 7+28 = 35

So I choose C.

Posted from my mobile device

urshi · Answer

ANSWER - OPTION C

P:H = 4x:5x 
Total animals in stable on Sunday - 9x

Total animals in stable on Monday - 9x+35 = 13y -- (1) (5y+8y = 13y)

So let's start with Option C

H = 60 . This implies X = 12

Equation (1) becomes 143 and hence divisible by 13. Hence we can eliminate Options D & E

Option A & B gives X = 11 & 7 respectively

So the total number of animals on Monday will be 134 & 98, both not divisible by 13 according to equation (1)

Hence , ANSWER - OPTION C

Posted from my mobile device

kush09 · Answer

Solution:  
 Let animal on Sunday be, 4x+5x (as per ponies and horses ration)
and animal on Monday be, 5y+8y (as per ponies and horses ration), after adding 35 animals,
=> 5y+8y=4x+5x+35
=> 13y = 9x + 35

x and y should be integers as they represent animals, we will go will option to find least value of x and y.

A. 35
 => x = 7 (35/5)
=> 13y = 63+35
=> 13y = 98,   y is not integer.

B. 55
 => x = 11 (55/5)
=> 13y = 99+35
=> 13y = 134,   y is not integer.

C. 60
=> x = 12 (35/5)
=> 13y = 108+35
=> 13y = 143, y =11.  
 
 C is the answer , we need not to calculate further as other values are bigger that 60

D. 65
E. 70

AliciaSierra · Answer

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

This question was provided by GMATWhiz
for the Heroes of Timers Competition

Show Answer

Official Answer

C

A. 35
B. 55
C. 60
D. 65
E. 70

Answer should be C.

Let's consider Ponies as P and Horses as H. We know that on Sunday P:H = 4:5. And after adding 35 more ponies and horses on Monday, ratio of P & H changed to P:H= 5:8. Now we have to find out minimum number of Horses on Sunday. Then we have given answer choices.

So sum of number of ponies and horses available on Sunday + 35 should be divisible by 13 ( Ratio P:H on Monday after adding 35 more P & H becomes 5:8)

Nevernevergiveup · Answer

initial ponies be  4x  and initial horses be  5x 
let the horses added on monday be  y 
 \frac{(4x+y)}{(5x+35-y)}=\frac{5}{8} 
by cross multiplication we get
 32x+8y=25x+175-5y
7x+13y=175
x=25-\frac{13}{7}y 
 y  can only be  7  to give an integer value of x which is mandatory.
so  x=25-13=12 
horses are  12*5=60

hr1212 · Answer

Algebraic solution:

Let ponies be P and horses be H, and x be the number of horses added on Monday then 35-x would be the number of ponies added.

Before, P/H = 4/5 => 5P = 4H --- (1)

After, (P + 35 - x)/(H + x) = 5/8 => 8P = 5H + 13x - 280 --- (2)

Now, substituting P in both the equations by multiplying eq. (1) by 8 and eq. (2) by 5,

32H = 25H + 65x - 1400
7H = 65x - 1400
H = 65x/7 - 200

Now, x should be a multiple of 7, so min value of H would be the value which results into above equation becoming positive for the first time, so x can be,

x = 7 x 4 => H = 65*4 - 200 = 60

Answer : C

Confusion · Answer

Divide all options by 5 that will be the ratio factor for 4:5

A. 35/ 5= 7
B. 55/5= 11
C. 60/5 = 12
D. 65/5 = 13
E. 70/5 = 14
Now This factor * 9 + 35 should be divisible by 13

A. 63 + 35
B. 99 + 35
C. 108 + 35 = 143 yes - ans - bingo 
D. 13*9 = 13*9 + 35 not divisible by 13
E. 14*9 + 35 = 126+ 35 = 161 no

Dream009 · Answer

ANother way 4:5 is the ratio. Let ratio factor be x
9x + 35 = 13y (from the ratio 8:5)
=> 9x + 9 + 26 = 13y
=> 9(x+1) + 26 = 13y
=> x+ 1 should be divisible by 13
From options divide all by 5 to x and add 1 to each

A. 35/ 5 + 1= 8
B. 55/5 + 1= 12
C. 60/5 + 1= 13 --- answer
D. 65/5 + 1 = 14
E. 70/5 + 1 = 15

HOT Competition: On Sunday, in Alexa’s stable, the ratio of the number

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HOT Competition: On Sunday, in Alexa’s stable, the ratio of the number

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards