Problem Solving

I did not clearly understand how to approach this and ended up guessing. Please help...

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 Icelandic. If there are 3 more horses than ponies, what is the minimum number of horses and ponies combined on the ranch?
A. 12
B. 21
C. 27
D. 39
E. 57

ncavaggn wrote:I did not clearly understand how to approach this and ended up guessing. Please help...

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 Icelandic. If there are 3 more horses than ponies, what is the minimum number of horses and ponies combined on the ranch?
A. 12
B. 21
C. 27
D. 39
E. 57

# of Ponies with Horseshoes (PH)= 5/6 * # of Ponies (P)
# of Ponies with Horseshoes that are Icelandic (PHI)= 2/3 * PH
=> PHI = 2/3 * 5/6 * P = 10/18 * P
Since we want exact number (integer value) of PH & PHI , P has to be a multiple of 18
Therefore minimum value of P will be 18
# of Horses = P + 3 = 18 + 3 = 21

Minimum # of horses and ponies combined = 21 + 18 = 39

The correct answer is D

Thanks,
I was simplifying (10/18) to (5/9) and taking only the multiple of 9, hence reaching a wrong minimum (15)!!
But, 5/6* (PH) also ahould be an integer.

ncavaggn wrote:Thanks,
I was simplifying (10/18) to (5/9) and taking only the multiple of 9, hence reaching a wrong minimum (15)!!
But, 5/6* (PH) also ahould be an integer.

Yes ... that was the trick