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The average (arithmetic mean) score of b quizzes for a group of studen

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The average (arithmetic mean) score of b quizzes for a group of studen [#permalink]

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New post 08 Jan 2018, 22:59
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The average (arithmetic mean) score of b quizzes for a group of students is 6.4. When one quiz score is discarded, the average of the remaining quiz scores becomes 4.8. What is the discarded quiz score?

A. 1.6b ­­­­­­+ 24
B. 1.6b – 4.8
C. 1.6b + 4.8
D. 6.4b – 24
E. 6.4b +4.8
[Reveal] Spoiler: OA

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The average (arithmetic mean) score of b quizzes for a group of studen [#permalink]

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New post 08 Jan 2018, 23:28
Bunuel wrote:
The average (arithmetic mean) score of b quizzes for a group of students is 6.4. When one quiz score is discarded, the average of the remaining quiz scores becomes 4.8. What is the discarded quiz score?

A. 1.6b ­­­­­­+ 24
B. 1.6b – 4.8
C. 1.6b + 4.8
D. 6.4b – 24
E. 6.4b +4.8


Let the total score of b quizzes be x.

From the question stem, we have \(\frac{x}{b}\) = 6.4 => x = 6.4b -> (1)

When including the discarded score, \(\frac{x-A}{b-1}\) = 4.8 where A is the discarded score.
Substituting the value of x from equation (1), we get \(\frac{6.4b-A}{b-1} = 4.8\)

Simplifying, we get \(6.4b - A = 4.8(b-1) = 4.8b - 4.8\)

Therefore, the discarded score A = 6.4b - (4.8b - 4.8) = 1.6b + 4.8(Option C)
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Re: The average (arithmetic mean) score of b quizzes for a group of studen [#permalink]

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New post 08 Jan 2018, 23:29
Bunuel wrote:
The average (arithmetic mean) score of b quizzes for a group of students is 6.4. When one quiz score is discarded, the average of the remaining quiz scores becomes 4.8. What is the discarded quiz score?

A. 1.6b ­­­­­­+ 24
B. 1.6b – 4.8
C. 1.6b + 4.8
D. 6.4b – 24
E. 6.4b +4.8


\((6.4b - x)/ (b-1) = 4.8\)
x = 1.6b + 4.8
C
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Re: The average (arithmetic mean) score of b quizzes for a group of studen [#permalink]

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New post 10 Jan 2018, 00:58
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(6.4b-X)/b-1 =4.8
X= 1.6+4.8
so, C
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Re: The average (arithmetic mean) score of b quizzes for a group of studen [#permalink]

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New post 10 Jan 2018, 07:45
Bunuel wrote:
The average (arithmetic mean) score of b quizzes for a group of students is 6.4. When one quiz score is discarded, the average of the remaining quiz scores becomes 4.8. What is the discarded quiz score?

A. 1.6b ­­­­­­+ 24
B. 1.6b – 4.8
C. 1.6b + 4.8
D. 6.4b – 24
E. 6.4b +4.8


\(\frac{6.4b - d}{( b -1 )} = 4.8\)

\(6.4b - d = 4.8b - 4.8\)

Or, \(1.6b + 4.8 = d\)

So, the discarded quiz score is 1.6b + 4.8 , answer will be (C)
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Re: The average (arithmetic mean) score of b quizzes for a group of studen [#permalink]

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New post 10 Jan 2018, 10:26
average = total sum / total q

1) 6.4 = x/b = 6.4b-x
2) 4.8 = x/b-1 = 4.8b - 4.8 - x

6.4b-x=4.8b-4.8-x
1.6b+4.8
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The average (arithmetic mean) score of b quizzes for a group of studen [#permalink]

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New post 10 Jan 2018, 10:45
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Bunuel wrote:
The average (arithmetic mean) score of b quizzes for a group of students is 6.4. When one quiz score is discarded, the average of the remaining quiz scores becomes 4.8. What is the discarded quiz score?

A. 1.6b ­­­­­­+ 24
B. 1.6b – 4.8
C. 1.6b + 4.8
D. 6.4b – 24
E. 6.4b +4.8

A*n = S

First set of scores
A = 6.4, n = b
Sum, S = 6.4b

Second set, one quiz discarded
A = 4.8, n = (b - 1)
Sum, S = 4.8(b - 1) = (4.8b - 4.8)

The difference in sums is the discarded score:
6.4b - (4.8b - 4.8) =
6.4b - 4.8b + 4.8 =
1.6b + 4.8

Answer C

Algebra is faster, but if you're really stuck, assign values.

(Average, A) * (number of terms,n) = Sum, S

Let b = 2

Then the sum for the first set of scores is A*n = S: (6.4 * 2) = 12.8
One score is removed. Number, n, of scores is now (2-1)= 1
Sum for second set of scores:(4.8 * 1) = 4.8

The score that was removed is
(Sum1 - Sum 2) = (12.8 - 4.8) = 8

With b = 2, find the answer that yields 8
Discard A and E (they are huge)
Discard B and D (with a little mental math, it's clear they're negative)
Answer C by POE. CHECK

C. 1.6b + 4.8
(1.6)(2) + 4.8 = (3.2 + 4.8) = 8 MATCH

Answer C
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The average (arithmetic mean) score of b quizzes for a group of studen   [#permalink] 10 Jan 2018, 10:45
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