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19 Feb 2024, 09:34
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B
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What is the average (arithmetic mean) number of runs per game scored by The New York Yankees last season?
(1) Last season, The New York Yankees played 160 games.
(2) Last season, The New York Yankees scored four runs per game in exactly \(\frac{1}{5}\) of their games, five runs per game in exactly \(\frac{3}{4}\) of their games, and nine runs per game in exactly \(\frac{1}{20}\) of their games.
(1) Last season, The New York Yankees played 160 games.
(2) Last season, The New York Yankees scored four runs per game in exactly \(\frac{1}{5}\) of their games, five runs per game in exactly \(\frac{3}{4}\) of their games, and nine runs per game in exactly \(\frac{1}{20}\) of their games.
19 Feb 2024, 09:34
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Official Solution:
What is the average (arithmetic mean) number of runs per game scored by The New York Yankees last season?
(1) Last season, The New York Yankees played 160 games.
This statement is clearly insufficient, as we don't know the total number of runs.
(2) Last season, The New York Yankees scored four runs per game in exactly \(\frac{1}{5}\) of their games, five runs per game in exactly \(\frac{3}{4}\) of their games, and nine runs per game in exactly \(\frac{1}{20}\) of their games.
Let's check what the sum of the fractions mentioned totals to.
Hence, we have the number of runs for each fraction of games which sum up to a total of 1. Thus, assuming the total games to be \(x\), we can calculate the average:
\(x\) gets reduced and we get:
Sufficient.
Answer: B
What is the average (arithmetic mean) number of runs per game scored by The New York Yankees last season?
(1) Last season, The New York Yankees played 160 games.
This statement is clearly insufficient, as we don't know the total number of runs.
(2) Last season, The New York Yankees scored four runs per game in exactly \(\frac{1}{5}\) of their games, five runs per game in exactly \(\frac{3}{4}\) of their games, and nine runs per game in exactly \(\frac{1}{20}\) of their games.
Let's check what the sum of the fractions mentioned totals to.
- \(\frac{1}{5} + \frac{3}{4} + \frac{1}{20} = 1\)
Hence, we have the number of runs for each fraction of games which sum up to a total of 1. Thus, assuming the total games to be \(x\), we can calculate the average:
- \(\frac{\frac{1}{5}*x*4 + \frac{3}{4}*x*5 + \frac{1}{20}*x*9}{x}\)
\(x\) gets reduced and we get:
- \(\frac{1}{5}*4 + \frac{3}{4}*5 + \frac{1}{20}*9 = 5\)
Sufficient.
Answer: B
06 Jul 2024, 00:37
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can someone help me to explain how we have the formula in (2) please? I don't know the relationship and how to conduct 4,5 and 9 in this formula
