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# In a certain school the student body has one-fifth seniors. If all the

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
In a certain school the student body has one-fifth seniors. If all the [#permalink]

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22 Dec 2017, 10:09
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35% (medium)

Question Stats:

79% (01:13) correct 21% (02:03) wrong based on 29 sessions

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In a certain school the student body has one-fifth seniors. If all the students were at a pep rally and forty percent of the seniors left the pep rally early, what was the percent change in the number of students at the rally?

A. 8%
B. 12%
C. 20%
D. 40%
E. 60%
[Reveal] Spoiler: OA

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Joined: 24 Nov 2016
Posts: 148
Re: In a certain school the student body has one-fifth seniors. If all the [#permalink]

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23 Dec 2017, 08:11
Bunuel wrote:
In a certain school the student body has one-fifth seniors. If all the students were at a pep rally and forty percent of the seniors left the pep rally early, what was the percent change in the number of students at the rally?

A. 8%
B. 12%
C. 20%
D. 40%
E. 60%

Before the seniors left, the proportion of all students was: $$Students.Before=Seniors+Others=\frac{1}{5}+\frac{4}{5}=0.20+0.80=1$$

After the seniors left, the proportion of all students was: $$Students.After=Seniors+Others={\frac{1}{5}*(1-\frac{2}{5})}+\frac{4}{5}=0.20*0.60+0.80=0.92$$

The percentage change is: $$\frac{Before-After}{Before}=\frac{1-0.92}{1}=0.08=$$$${8%}$$

(A) is the answer.
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In a certain school the student body has one-fifth seniors. If all the [#permalink]

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23 Dec 2017, 11:32
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KUDOS
Bunuel wrote:
In a certain school the student body has one-fifth seniors. If all the students were at a pep rally and forty percent of the seniors left the pep rally early, what was the percent change in the number of students at the rally?

A. 8%
B. 12%
C. 20%
D. 40%
E. 60%

Assume the total number of students to be 1000.

As the student body has one-fifth seniors, the number will be 200.
Since 40% of the seniors left the pep rally, 40% of 200 or 0.4*200 = 80 seniors leave the pep rally.

Hence, the percentage change of number of students in the pep rally will be from 1000 to 920 (8% - Option A)

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