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15 Nov 2021, 03:43
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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.
(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.
15 Nov 2021, 03:43
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Official Solution:
On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 lamas on the farm?
\(\frac{pigs }{ostriches }=\frac{7}{5}\)
(1) The ratio of ostriches to lamas is 4 to 3.
\(\frac{ostriches }{lamas }=\frac{4}{3}=\frac{20}{15}\)
\(\frac{pigs }{ostriches }=\frac{7}{5}=\frac{28}{20}\)
So, \(pigs:ostriches:lamas=28:20:15\). The minimum number of lamas is therefore 15. Sufficient.
(2) There are five more ostriches than lamas, and there are 8 more pigs than ostriches.
There are 8 more pigs than ostriches: \(7x - 5x=8\). This gives \(x=4\). So, the number of ostriches is \(5x=20\), and therefore the number of lamas is \(20-5=15\). Sufficient.
Answer: D
On a certain farm, the ratio of pigs to ostriches is 7 to 5. Are there more than 14 lamas on the farm?
\(\frac{pigs }{ostriches }=\frac{7}{5}\)
(1) The ratio of ostriches to lamas is 4 to 3.
\(\frac{ostriches }{lamas }=\frac{4}{3}=\frac{20}{15}\)
\(\frac{pigs }{ostriches }=\frac{7}{5}=\frac{28}{20}\)
So, \(pigs:ostriches:lamas=28:20:15\). The minimum number of lamas is therefore 15. Sufficient.
(2) There are five more ostriches than lamas, and there are 8 more pigs than ostriches.
There are 8 more pigs than ostriches: \(7x - 5x=8\). This gives \(x=4\). So, the number of ostriches is \(5x=20\), and therefore the number of lamas is \(20-5=15\). Sufficient.
Answer: D
22 Apr 2023, 12:00
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Bunuel
Hi Bunuel
If "x" denotes the total number of animals (Pigs + Ostriches + Lamas) then how can we use the ratio of P:O = 7:5 to arrive at the equation \(7x - 5x=8\)?
Moreover, if we use the ratio P:O=7:5 shouldn't the equation be \(\frac{7x-5x}{12}=8\)
