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05 Feb 2022, 04:06
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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 1/5 of their games, five runs per game in exactly 3/4 of their games, and nine runs per game in exactly 1/20th 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 1/5 of their games, five runs per game in exactly 3/4 of their games, and nine runs per game in exactly 1/20th of their games.
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19 Feb 2024, 09:36
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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.
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
(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
General Discussion
kungfury42
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05 Feb 2022, 13:39
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(1) The fact that New York Yankees played a total of 160 games gives us no clue into the total number of runs that they may have scored. Maybe they scored 0 runs in each game, maybe they scored 100 runs in each game, or maybe they scored runs in an AP from 1 to 160 in their 160 games. We can't say which case it was. There's literally a bazillion possibilities. Hence, statement 1 is insufficient. Eliminate options A and D.
(2) Let's assume the New York Yankees played a total of n games.
Now we know that they scored 4 runs on average in exactly 1/5th of their games. So we know that the total runs scored by them across these 0.2n games are 0.2n*4 = 0.8n
Similarly, goal runs scored by them in next 3/4th or 0.75n games at an average of 5 runs per game are 0.75n*5 = 3.75n
Likewise, we'll have a total of 0.05n*9 = 0.45n runs scored by them in the next 1/20th of their games.
Hence, total runs scored across n games = 0.8n + 3.75n + 0.45n = 5n
Therefore, average runs scored per game = 5n/n = 5
Hence, statement 2 alone is sufficient, and our answer is option B.
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(2) Let's assume the New York Yankees played a total of n games.
Now we know that they scored 4 runs on average in exactly 1/5th of their games. So we know that the total runs scored by them across these 0.2n games are 0.2n*4 = 0.8n
Similarly, goal runs scored by them in next 3/4th or 0.75n games at an average of 5 runs per game are 0.75n*5 = 3.75n
Likewise, we'll have a total of 0.05n*9 = 0.45n runs scored by them in the next 1/20th of their games.
Hence, total runs scored across n games = 0.8n + 3.75n + 0.45n = 5n
Therefore, average runs scored per game = 5n/n = 5
Hence, statement 2 alone is sufficient, and our answer is option B.
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