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# At a public housing conference 15 percent of the attendees are male.

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At a public housing conference 15 percent of the attendees are male. [#permalink]

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20 Oct 2017, 00:10
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25% (medium)

Question Stats:

82% (01:31) correct 18% (01:16) wrong based on 66 sessions

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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
[Reveal] Spoiler: OA

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Re: At a public housing conference 15 percent of the attendees are male. [#permalink]

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20 Oct 2017, 00:19
Total initial number: x
Male: 0,15x
Female: 0,85x
Female left: y
New Female: 0,85x-y
New Total: 0,6x

0,15x+0,85x-y=0,6x
y=0,4x

fraction of new female from initial number:

0,4x/0,85x=8/17

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Re: At a public housing conference 15 percent of the attendees are male. [#permalink]

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20 Oct 2017, 09:58
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Let the total number of attendees be 100.
No. of male attendees = 15
No. of female attendees = 85
Some female attendees left, then % remaining =60%
Number of attendees remaining = 60
The number of female attendees who leave =100-60=40
Fraction of the number of female attendees who leave to the original number of females attending the conference
=$$\frac{40}{85}$$ =$$\frac{8}{17}$$

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Re: At a public housing conference 15 percent of the attendees are male. [#permalink]

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20 Oct 2017, 14:26
Let the number of people at this conference be 100.
-15 are male which implies 85 are female.
-Only women leave and we're left with 60 people, this implies 40 women left the conference.
-[85-40][/85] this simplifies to [8][/17]
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Re: At a public housing conference 15 percent of the attendees are male. [#permalink]

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21 Oct 2017, 00:53
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

Let total attendees = 100
Male = 15
Female = 85

Number of attendees left = 60
Male = 15
Female = 45
Female left = 85-45 = 40

Required fraction = 40/85 = 8/17

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Re: At a public housing conference 15 percent of the attendees are male. [#permalink]

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24 Oct 2017, 06:42
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 are male.   [#permalink] 24 Oct 2017, 06:42
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