Ratio Proportion--- easy or alternate approach ?

[guerrero]

Experts please help

Both the Smith horse farm and the Windsor horse farm have Appaloosa, Chestnut, and Palomino horses. At the Smith horse farm, the Appaloosa to Chestnut ratio is 1:4, and the Chestnut to Palomino ratio is 1:2. At the Windsor horse farm, the Appaloosa to Chestnut ratio is 1:5. Together, the two farms have 45 Chestnut horses. Which of the following could be the number of Appaloosa horses that the Smith farm has?

ANS a) 5 b)7 c)8 d)9 e) 11

Source: Kaplan test

I could not solve the problem during the test , When going through the solution I felt it was a long approach . Can any one help me with an alternate approach for this kind of problem ?

Thank you in anticipation .

[anuprajan5]

The answer is A

Smith farm - the ratios can be set in 1:4:8 ration for A:C:P horses.

Windsor farm - the ratio is 1:5 for A:C

C horses on both farms total to 45.

Therefore, assume the common factor for Smith farm is x and for Windsor farm is y.

4x+5y = 45
There are only 2 viable solutions, where x = 10, y = 1 and x=5 and y = 5

Plugging this into the ratio, then

[spoiler]Smith farm A:C:P could be 10:40:80 or 5:20:40. Answer choice reflects A as 5[/spoiler]

[GMATGuruNY]

Experts please help

Both the Smith horse farm and the Windsor horse farm have Appaloosa, Chestnut, and Palomino horses. At the Smith horse farm, the Appaloosa to Chestnut ratio is 1:4, and the Chestnut to Palomino ratio is 1:2. At the Windsor horse farm, the Appaloosa to Chestnut ratio is 1:5. Together, the two farms have 45 Chestnut horses. Which of the following could be the number of Appaloosa horses that the Smith farm has?

ANS a) 5 b)7 c)8 d)9 e) 11

Smith Chestnuts + Windsor Chestnuts = 45.
The TOTAL number of Chestnuts (45) is a multiple of 5.
At Windsor, A:C = 1:5, implying that number of WINDSOR Chestnuts is a multiple of 5.
Thus:
Smith Chestnuts + (multiple of 5) = (multiple of 5).
The implication is that the number of SMITH Chestnuts must also be a multiple of 5.

At Smith, A:C = 1:4,
Since the actual number of Chestnuts here must be a multiple of 5, only two cases are possible:
A:C = 5(1:4) = 5:20.
A:C = 10(1:4) = 10:40.
Only the first case -- 5 Appaloosa -- is among the answer choices.

The correct answer is A.