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The average (arithmetic mean) score of x students on a certain exam is

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The average (arithmetic mean) score of x students on a certain exam is 81. If one additional student takes the exam and scores a 99, the average score will increase to 83. What is the value of x ?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
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Re: The average (arithmetic mean) score of x students on a certain exam is [#permalink]

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New post 04 Feb 2017, 04:49
SajjadAhmad wrote:
The average (arithmetic mean) score of x students on a certain exam is 81. If one additional student takes the exam and scores a 99, the average score will increase to 83. What is the value of x ?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


Intial average = 81 Final average = 83. Increase in average = 2 marks/student.

Marks of new student = 99, Marks above average = 99 - 83 = 16 . Hence x = 16/2 = 8.

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Re: The average (arithmetic mean) score of x students on a certain exam is [#permalink]

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SajjadAhmad wrote:
The average (arithmetic mean) score of x students on a certain exam is 81. If one additional student takes the exam and scores a 99, the average score will increase to 83. What is the value of x ?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


81x + 99 = (x + 1 ) 83

Or, 81x + 99 = 83x + 83

Or, 16 = 2x

Or, x = 8

Hence, the value of x is 8
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The average (arithmetic mean) score of x students on a certain exam is [#permalink]

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New post 04 Feb 2017, 09:06
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SajjadAhmad wrote:
The average (arithmetic mean) score of x students on a certain exam is 81. If one additional student takes the exam and scores a 99, the average score will increase to 83. What is the value of x ?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


Let's plug in some "nice" values for the test results.

The average (arithmetic mean) score of x students on a certain exam is 81
So, one possibility is that EACH of those x students received a score of 81.
So, the TOTAL SUM of all x scores = 81x

If one additional student takes the exam and scores a 99, the average score will increase to 83. What is the value of x ?
With this additional score, we now have x + 1 scores
Also, the TOTAL SUM of all x +1 scores = 81x + 99

Since the new average is 83, we can write: (81x + 99)/(x + 1) = 83
Multiply both sides by (x+1) to get: 81x + 99 = 83(x + 1)
Expand: 81x + 99 = 83x + 83
Rearrange: 16 = 2x
Solve: x = 8

Answer: B

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