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The average (arithmetic mean) of a set of n test scores is 8

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The average (arithmetic mean) of a set of n test scores is 8 [#permalink] New post 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.

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[Reveal] Spoiler: OA

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Re: The average (arithmetic mean) of a set of n test scores is 8 [#permalink] New post 09 Mar 2020, 08:44
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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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Re: The average (arithmetic mean) of a set of n test scores is 8 [#permalink] New post 06 Apr 2020, 13:18
would you define this question as one of the hard ones?
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Re: The average (arithmetic mean) of a set of n test scores is 8 [#permalink] New post 06 Apr 2020, 15:12
Expert's post
mike1917 wrote:
would you define this question as one of the hard ones?


IMO, it's more of a medium question. I'd place it in the 150 to 155 range.

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Brent
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Re: The average (arithmetic mean) of a set of n test scores is 8 [#permalink] New post 06 Apr 2020, 15:39
Expert's post
The tag medium rather than hard comes directly from the book.

Of course, at the time a question like this was pretty hard but over time became medium.

The level has decreased.

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Re: The average (arithmetic mean) of a set of n test scores is 8   [#permalink] 06 Apr 2020, 15:39
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