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06 Apr 2022, 04:00
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Difficulty:
95%
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Question Stats:
47% (02:25) correct
53%
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wrong
based on 156
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A bicycle store earned a different percent profit on each of the three models of bicycles it sells, as shown in the table above. If the store made a total profit of 16% on sales of these three models of bicycles last month, and these three models represented the entirety of the store’s profits, what percent of its total profits last month came from sales of Model A bicycles?
(1) The store earned 20% of its profits last month from sales of Model B bicycles.
(2) The store earned 50% of its profits last month from sales of Model C bicycles.
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11 Apr 2022, 03:27
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Question: What percent of its total profits last month came from sales of Model A bicycles
Let A, B, and C be the sales of Model A, Model B, and Model C respectively.
The company makes a total profit of 16% on sales of these three models of bicycles last month.
Total profit = \(\frac{16}{100}\) (A + B + C)
Total profit can also be computed as the sum of profits from individual models.
i.e., Total Profit = Profit from model A + Profit from model B + Profit from model C
\(\frac{16}{100}\)(A + B + C) = \(\frac{12}{100}\)A + \(\frac{16}{100}\)B + \(\frac{20}{100}\)C
\(\frac{16}{100}\)(A + C) = \(\frac{12}{100}\)A + \(\frac{20}{100}\)C
We get, A = C
i.e., Sales of A = Sales of C
Statement-1: The store earned 20% of its profits last month from sales of Model B bicycles.
Profit from sales of Model B = 20% of total profit
\(\frac{16}{100}\)B =\( \frac{20}{100}*\frac{16}{100}\) (A + B + C)
1600B = 320A + 320B + 320C
From question stem, we know A = C. Therefore, 1280B = 640A
Or 2B = A
Profit from sales of model A = \(\frac{12}{100}\)A = \(\frac{12}{100}\)2B
Or Profit from sales of model A = \(\frac{24}{100}\)B
Profit from sales of model B = \(\frac{16}{100} \)B = 20% of overall profit
If \(\frac{16}{100} \)B = 20% of overall profit, then \(\frac{24}{100}\)B = 30% of overall profit.
We are able to find profit from sale of Model A as a percentage of total profit.
So Statement 1 alone is sufficient. Answer is option A or option D.
Statement-2: The store earned 50% of its profits last month from sales of Model C bicycles.
Profit from sales of Model C = 50% of total profit
\(\frac{20}{100} \)C = 50% of total profit
From question stem, we know C = A
\(\frac{20}{100}\) A = 50% of total profit
Profit from sales of model A = \(\frac{12}{100}\) A
If \(\frac{20}{100}\) A equals 50% of total profit, then \(\frac{12}{100}\) A will equal 30% of total profit.
So Statement 2 alone is sufficient.
Each statement is independently sufficient to answer the question.
Answer is Choice D
Let A, B, and C be the sales of Model A, Model B, and Model C respectively.
The company makes a total profit of 16% on sales of these three models of bicycles last month.
Total profit = \(\frac{16}{100}\) (A + B + C)
Total profit can also be computed as the sum of profits from individual models.
i.e., Total Profit = Profit from model A + Profit from model B + Profit from model C
\(\frac{16}{100}\)(A + B + C) = \(\frac{12}{100}\)A + \(\frac{16}{100}\)B + \(\frac{20}{100}\)C
\(\frac{16}{100}\)(A + C) = \(\frac{12}{100}\)A + \(\frac{20}{100}\)C
We get, A = C
i.e., Sales of A = Sales of C
Statement-1: The store earned 20% of its profits last month from sales of Model B bicycles.
Profit from sales of Model B = 20% of total profit
\(\frac{16}{100}\)B =\( \frac{20}{100}*\frac{16}{100}\) (A + B + C)
1600B = 320A + 320B + 320C
From question stem, we know A = C. Therefore, 1280B = 640A
Or 2B = A
Profit from sales of model A = \(\frac{12}{100}\)A = \(\frac{12}{100}\)2B
Or Profit from sales of model A = \(\frac{24}{100}\)B
Profit from sales of model B = \(\frac{16}{100} \)B = 20% of overall profit
If \(\frac{16}{100} \)B = 20% of overall profit, then \(\frac{24}{100}\)B = 30% of overall profit.
We are able to find profit from sale of Model A as a percentage of total profit.
So Statement 1 alone is sufficient. Answer is option A or option D.
Statement-2: The store earned 50% of its profits last month from sales of Model C bicycles.
Profit from sales of Model C = 50% of total profit
\(\frac{20}{100} \)C = 50% of total profit
From question stem, we know C = A
\(\frac{20}{100}\) A = 50% of total profit
Profit from sales of model A = \(\frac{12}{100}\) A
If \(\frac{20}{100}\) A equals 50% of total profit, then \(\frac{12}{100}\) A will equal 30% of total profit.
So Statement 2 alone is sufficient.
Each statement is independently sufficient to answer the question.
Answer is Choice D
22 Jan 2026, 13:04
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