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# Sixty percent of the people who originally auditioned for parts in a m

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Math Expert
Joined: 02 Sep 2009
Posts: 55228
Sixty percent of the people who originally auditioned for parts in a m  [#permalink]

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29 Nov 2018, 01:18
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Difficulty:

5% (low)

Question Stats:

93% (01:51) correct 7% (01:41) wrong based on 31 sessions

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Sixty percent of the people who originally auditioned for parts in a musical were excused, and the rest were asked to audition again. Of those who were asked to audition again, 30 percent, or 18 people, were hired. How many people originally auditioned for parts?

A. 150
B. 120
C. 100
D. 60
E. 30

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Re: Sixty percent of the people who originally auditioned for parts in a m  [#permalink]

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29 Nov 2018, 04:19
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Bunuel wrote:
Sixty percent of the people who originally auditioned for parts in a musical were excused, and the rest were asked to audition again. Of those who were asked to audition again, 30 percent, or 18 people, were hired. How many people originally auditioned for parts?

A. 150
B. 120
C. 100
D. 60
E. 30

x*30/100= 18
x= 60 original who were 2nd time auditioned

so 60=x*40/100
x= 150 total no IMO A
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Re: Sixty percent of the people who originally auditioned for parts in a m  [#permalink]

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29 Nov 2018, 17:28
Top Contributor
Bunuel wrote:
Sixty percent of the people who originally auditioned for parts in a musical were excused, and the rest were asked to audition again. Of those who were asked to audition again, 30 percent, or 18 people, were hired. How many people originally auditioned for parts?

A. 150
B. 120
C. 100
D. 60
E. 30

Let x = number of people who ORIGINALLY auditioned.

Sixty percent of the people who originally auditioned for parts in a musical were excused . . .
If 60% were EXCUSED (sent home), then 40% of the people REMAINED
So, the number of people remaining = 40% of x = 0.4x

. . . and the rest (aka the REMAINING people) were asked to audition again. Of those who were asked to audition again, 30 percent, or 18 people, were hired.
30% of the remaining people were hired
In other words, number of people hired = 30% of 0.4x
= (0.3)0.4x
= 0.12x

We're told that 18 people were hired.
We can write: 0.12x = 18
Solve: x = 18/0.12 = 150

So, 150 people originally auditioned.

Cheers,
Brent
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Re: Sixty percent of the people who originally auditioned for parts in a m   [#permalink] 29 Nov 2018, 17:28
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