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# If 15 students in a class average 80% on an English exam and 10 studen

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Math Expert
Joined: 02 Sep 2009
Posts: 55715
If 15 students in a class average 80% on an English exam and 10 studen  [#permalink]

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24 Jan 2016, 05:46
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:26) correct 11% (01:36) wrong based on 86 sessions

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If 15 students in a class average 80% on an English exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?

A. 83%
B. 83 1⁄2%
C. 84%
D. 85%
E. 86 2⁄3%

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Joined: 19 Jan 2016
Posts: 45
Re: If 15 students in a class average 80% on an English exam and 10 studen  [#permalink]

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24 Jan 2016, 21:10
1
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Bunuel wrote:
If 15 students in a class average 80% on an English exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?

A. 83%
B. 83 1⁄2%
C. 84%
D. 85%
E. 86 2⁄3%

The average percentage = (15 x 80% + 10 x 90%)/25
= (15 x 80% + 10x 80% + 10x10%) / 25 ......(as 90% = 10% + 80% )
=(25x80% + 10x10%)/25
= 80% + 10x10%/25
= 80% + 4%
= 84%

==> C
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Math Expert
Joined: 02 Aug 2009
Posts: 7756
If 15 students in a class average 80% on an English exam and 10 studen  [#permalink]

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24 Jan 2016, 21:42
Bunuel wrote:
If 15 students in a class average 80% on an English exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?

A. 83%
B. 83 1⁄2%
C. 84%
D. 85%
E. 86 2⁄3%

Hi,
there could be two ways to these Qs..

1) intensive calculations :-
we multiply the averages with number, add the two and again find average..
15 students have 80% average..
lets take 80% as 80 marks,as we are dealing with only %..
so total marks=15*80=1200..
similarly 10 students 90 average marks= 10*90=900..
total marks= 1200+900=2100..
students=25, so average= 2100/25= 84%..

2) weighted average:- A better way with less calculations..
we have 15:10 students with 80:90 average %..
the final average will depend on the ratio of students and will be closer to the average with more students..
so the fraction/ratio of students with 90% marks= 10/(10+15)=2/5..

The final average will be (1-2/5)* the difference of the averages from 90%..
so 3/5*10=6 away from 90.. 90-6=84
C
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If 15 students in a class average 80% on an English exam and 10 studen  [#permalink]

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16 Dec 2016, 18:53
Here is my solution to this one->

Let maximum marks allocated be 100

Hence Using the mean law=> $$Mean = \frac{Sum}{#}$$

Sum(15)=80*15=1200
Sum(10)=90*10=900

Hence Sum(25)=1200+900=2100
Thus mean = 2100/25 = 84

84 is 84 percent of 100

Hence C

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Posts: 991
Re: If 15 students in a class average 80% on an English exam and 10 studen  [#permalink]

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16 Dec 2016, 19:42
Bunuel wrote:
If 15 students in a class average 80% on an English exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?

A. 83%
B. 83 1⁄2%
C. 84%
D. 85%
E. 86 2⁄3%

weighted avg. method to be used(shown above by chetan )

w1/w2=a1-avg./avg.-a2

15/10=90-x/x-80
x=84

Ans C
Manager
Joined: 25 May 2016
Posts: 85
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V30
Re: If 15 students in a class average 80% on an English exam and 10 studen  [#permalink]

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03 Jan 2018, 02:50
we can use the ratio 15:10 = 3:2
3*80 + 2*90 = 420
420/5=84

Option C, slightly simpler calculation using this method.
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Re: If 15 students in a class average 80% on an English exam and 10 studen   [#permalink] 03 Jan 2018, 02:50
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