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# If each of the bowlers in a tournament bowled an equal number of games

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If each of the bowlers in a tournament bowled an equal number of games [#permalink]

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27 Dec 2015, 09:10
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If each of the bowlers in a tournament bowled an equal number of games, what is the average (arithmetic mean) score of all the games bowled in the tournament?

(1) 70 percent of the bowlers had an average (arithmetic mean) score of 120, and the other 30 percent had an average score of 140.
(2) Each of the 350 bowlers in the tournament bowled 3 games.
[Reveal] Spoiler: OA

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Re: If each of the bowlers in a tournament bowled an equal number of games [#permalink]

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28 Dec 2015, 12:37
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If each of the bowlers in a tournament bowled an equal number of games, what is the average (arithmetic mean) score of all the games bowled in the tournament?

(1) 70 percent of the bowlers had an average (arithmetic mean) score of 120, and the other 30 percent had an average score of 140.
(2) Each of the 350 bowlers in the tournament bowled 3 games.

From the original condition, we need to know the total number of bowlers (n) and the total score (s). In order to match the number of variables and the number of equations, we need 2 more equations. Since both 1) and 2) each has 1 equation, there is high chance C is the answer.

(Note: This is a statistics question, one of the key questions. Also, when the condition 1) has % and the condition 2) has a number, it is likely that the condition with % is going to be the answer.)

In a case of the condition 1), since the number of bowlers is n, from (0.7n*120+0.3n*140)/n, we get a unique answer and the condition is sufficient. Therefore, the answer is A. This is a type of question that appears within the score range of 50 and 51.

From con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.
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Re: If each of the bowlers in a tournament bowled an equal number of games [#permalink]

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29 Dec 2015, 03:36
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Bunuel wrote:
If each of the bowlers in a tournament bowled an equal number of games, what is the average (arithmetic mean) score of all the games bowled in the tournament?

(1) 70 percent of the bowlers had an average (arithmetic mean) score of 120, and the other 30 percent had an average score of 140.
(2) Each of the 350 bowlers in the tournament bowled 3 games.

Given: Each of the bowlers in a tournament bowled an equal number of games
Required: what is the average score of all the games bowled in the tournament

Hence, we need to find the ratio of the total score and the total players.

Statement 1: 70 percent of the bowlers had an average (arithmetic mean) score of 120, and the other 30 percent had an average score of 140
Assume total players to be 100x

Total score = 70x*120 + 30x*140
Average score = 70x*120 + 30x*140 / 100x
We can find the average score.
SUFFICIENT

Statement 2: Each of the 350 bowlers in the tournament bowled 3 games.
This does not tell any thing about the score.
INSUFFICIENT

Option A
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Re: If each of the bowlers in a tournament bowled an equal number of games   [#permalink] 29 Dec 2015, 03:36
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