Quote:
On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 llamas on the farm?
(1) The ratio of ostriches to llamas is 4 to 3.
(2) There are five more ostriches than llamas, and there are 8 more pigs than ostriches.
Solution: Let's consider Pigs= P , Ostriches=O , Llamas= L
From question stem we know
\(\frac{P}{O}=\frac{7}{5} =\frac{7X}{5X}\)
P can be 7, 14, 21, 28,35,42,49..... equation(1)
O can be 5,10,15,
20,25,30,35,40.... equation(2)
Option1.
\(\frac{Ostriches}{Llamas}=\frac{O}{I}=\frac{4}{3}=\frac{4Y}{3Y}\)
O= 4,8,12,16,
20,24.......40.... etc. --equation(3)
First common term between equation(2) and equation (3) is 20 so minimum number of Ostriches can be 20 i.e. 4*5. So minimum number of Llamas 3*5=15.
15>14.
Are there more than 14 llamas on the farm->YES
option2.
\(\frac{P}{O}=\frac{7X}{5X}\)
There are five more ostriches than llamas, and there are 8 more pigs than ostriches.
=>P=O+8=>7X=5X+8=>X=
4=>O=L+5 => 5X=L+5=> 5*
4=L+5 =>L=15
Are there more than 14 llamas on the farm->YES
Both options individually are sufficient get answer.
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