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# At a public housing conference 15 percent of the attendees a

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At a public housing conference 15 percent of the attendees a [#permalink]  18 Oct 2017, 22:52
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Question Stats:

66% (07:19) correct 33% (01:24) wrong based on 3 sessions
At a public housing conference 15 percent of the attendees are male. After the speaker finishes, several female attendees but no males leave the conference and the total number of persons remaining is 60 percent of the original number. The number of female attendees who leave is what fraction of the original number of females attending the conference?

(A) 11/20
(B) 9/17
(C) 8/17
(D) 9/20
(E) 2/5

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[Reveal] Spoiler: OA
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Re: At a public housing conference 15 percent of the attendees a [#permalink]  19 Oct 2017, 00:10
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Bunuel wrote:
At a public housing conference 15 percent of the attendees are male. After the speaker finishes, several female attendees but no males leave the conference and the total number of persons remaining is 60 percent of the original number. The number of female attendees who leave is what fraction of the original number of females attending the conference?

(A) 11/20
(B) 9/17
(C) 8/17
(D) 9/20
(E) 2/5

Kudos for correct solution.

Let take the total no. = 100
Now 15% of total is male = 15% *100 =15 male

Therefore women = 100 -15 =85

No. of person left after female left is 60% of Total = 60% *100 =60

In this 60 people 15 are male, so female = 45
So Female left = 85-45=40

Therefore the fraction of the female who left to the original females attending the conferance = $$\frac{40}{85}$$ = $$\frac{8}{17}$$
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Re: At a public housing conference 15 percent of the attendees a [#permalink]  08 Jan 2018, 11:04
Expert's post
Bunuel wrote:
At a public housing conference 15 percent of the attendees are male. After the speaker finishes, several female attendees but no males leave the conference and the total number of persons remaining is 60 percent of the original number. The number of female attendees who leave is what fraction of the original number of females attending the conference?

(A) 11/20
(B) 9/17
(C) 8/17
(D) 9/20
(E) 2/5

We can let 100 be the number of attendees originally at the conference. Thus, there are 15 males and 85 females. If only females have left and no males have left, and the total number of people remaining is 60, it must mean that 40 females have left. Therefore, the number of female attendees who have left is 40/85 = 8/17 of the original number of female attendees at the conference.

Alternate Solution:

Let’s let n = the original total number of attendees. Thus, 0.15n = the number of male attendees and 0.85 = the number of female attendees. Now, let’s let x = the number of females who leave. We have:

n - x = 0.6n

0.4n = x

We know that 0.4n is the number of females who left. Thus, the percentage of females who left, out of the total number of females who originally attended, is (0.4n)/(0.85n) = 40/85 = 8/17.

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Re: At a public housing conference 15 percent of the attendees a   [#permalink] 08 Jan 2018, 11:04
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