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# The average (arithmetic mean) of 16 students first quiz scores in a di

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Joined: 13 Sep 2016
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The average (arithmetic mean) of 16 students first quiz scores in a di  [#permalink]

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Updated on: 18 Sep 2016, 02:55
5
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:37) correct 23% (01:42) wrong based on 61 sessions

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The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 64.0. What is the quiz score of the student who dropped the class?

a) 10
b) 25
c) 40
d) 55
e) 70

Originally posted by Nanobotstv on 18 Sep 2016, 02:47.
Last edited by Bunuel on 18 Sep 2016, 02:55, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The average (arithmetic mean) of 16 students first quiz scores in a di  [#permalink]

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18 Sep 2016, 03:07
1
1
alanforde800Maximus wrote:
The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 64.0. What is the quiz score of the student who dropped the class?

a) 10
b) 25
c) 40
d) 55
e) 70

Total Score of 16 students is 16*62.50 = 1000

Total Score of 15 students is 15*64 = 960

So, the score of the person who left is 40 ( 1000 - 960 )

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Re: The average (arithmetic mean) of 16 students first quiz scores in a di  [#permalink]

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18 Sep 2016, 05:00
score of 16 students = 16*avg arithmetic mean = 16*62.5 = 1000
score of 15 students = 15*64 = 960
diff = 40
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Re: The average (arithmetic mean) of 16 students first quiz scores in a di  [#permalink]

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28 Jan 2018, 14:25
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Hi All,

This question is a 'weighted average' question that gives you all of the numbers to work with, so solving it with arithmetic (the way that Mitch did) is a pretty standard approach for this type of prompt. There's a built-in concept that you can take advantage of to save some time though.

The one score that was removed from the total was small enough that it raised the average of the remaining 15 scores from a 62.5 to a 64. That 1.5 point increase per person, in total, would be (1.5)(15) = 22.5 points.

So the removed score had to be 22.5 points lower than the original average: 62.5 - 22.5 = 40.

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Re: The average (arithmetic mean) of 16 students first quiz scores in a di  [#permalink]

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05 Mar 2019, 11:50
Sum of scores of 16 students = 62.5 * 16
Sum of scores of 15 students = 64 * 15

Sum of score of the student who left = 62.5 * 16 - 64 * 15= 16(62.5-60) = 16(2.5) = 40

To shorten the calculation *64 = 2x2x4x4 -> so you can take 16 common
Re: The average (arithmetic mean) of 16 students first quiz scores in a di   [#permalink] 05 Mar 2019, 11:50
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