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The average (arithmetic mean) of a set of n test scores is 8 [#permalink]
08 Mar 2020, 10:48

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The average (arithmetic mean) of a set of n test scores is 80. The average (arithmetic mean) of these n scores together with a score of 85 is 81.

Quantity A

Quantity B

\(n\)

\(5\)

A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.

Re: The average (arithmetic mean) of a set of n test scores is 8 [#permalink]
09 Mar 2020, 08:44

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Expert's post

Carcass wrote:

The average (arithmetic mean) of a set of n test scores is 80. The average (arithmetic mean) of these n scores together with a score of 85 is 81.

Quantity A

Quantity B

\(n\)

\(5\)

The average (arithmetic mean) of a set of n test scores is 80. We can write: (sum of all n test scores)/n = 80 Multiply both sides by n to get: sum of all n test scores = 80n

The average (arithmetic mean) of these n scores together with a score of 85 is 81. Once we add the score of 85 to the other n scores, we have a total of n+1 scores So, we can write: (sum of the n test scores + 85)/(n + 1) = 81 Substitute to get: (80n + 85)/(n + 1) = 81 Multiply both sides of the equation by (n + 1) to get: 80n + 85 = 81(n + 1) Expand: 80n + 85 = 81n + 81 Subtract 81 from both sides: 80n + 4 = 81n Subtract 80n from both sides: 4 = n

We get: QUANTITY A: 4 QUANTITY B: 5

Answer: B

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