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One-sixth of the attendees at a certain convention are [#permalink]

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01 Jun 2010, 05:14

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E

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Question Stats:

72% (01:39) correct
28% (01:50) wrong based on 525 sessions

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One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 150 of the attendees are neither female nor students, what is the total number of attendees at the convention?

Let no. of Attendee are A. Now As per the condition of the problem stated above .

We have following population in the convention as Attendee. Total no. of females = [2/3]*A Total no. of females as student : [1/6]*A Total no. of students = [1/3]*A Total no. of male as student = [1/6]*A Total no. of males = A - [2/3]*A = [1/3]A No. of males which are not student = [1/3]A - [1/6]*A = 150

Hence A = 900

Total no of males who are not student will be the answer as it states it should be neither female nor student So Answer is E
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One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 150 of the attendees are neither female nor students, what is the total number of attendees at the convention?

300 450 600 800 900

Didnt really understand the solution provided to this question.

Re: One-sixth of the attendees at a certain convention are [#permalink]

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22 Oct 2013, 12:16

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Re: One-sixth of the attendees at a certain convention are [#permalink]

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20 May 2014, 03:37

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Using Venn Diagram

Attachment:

File comment: Venn Diagram

gmat.jpg [ 25.25 KiB | Viewed 6503 times ]

Lets take number of total attendees as X.

Out of these, X/3 are students (represented by circle marked student), 2X/3 are female (represented by circle marked female) and X/3 are female students (represented by the overlapping area of both the circles)

From Venn Diagram, total number of attendees who are student , female or both will be given by

X/3 + 2X/3 - X/6 = 5X/6

Those who are not student or female = X - 5X/6 = X/6

Given that, number of attendees who are neither student nor female = 150

Re: One-sixth of the attendees at a certain convention are [#permalink]

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03 Feb 2016, 01:54

Hello from the GMAT Club BumpBot!

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Re: One-sixth of the attendees at a certain convention are [#permalink]

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11 Jul 2017, 07:01

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One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 150 of the attendees are neither female nor students, what is the total number of attendees at the convention?

A. 300 B. 450 C. 600 D. 800 E. 900

We can create the following equation:

Total = number of females + number of students - number of both + number of neither

We can let n = the number of attendees, and thus, (n/6) are female students (i.e., both). We also know that (2n/3) are females, (n/3) are students, and 150 of the attendees are neither female nor students. Thus:

n = (2n/3) + (n/3) - (n/6) + 150

Multiplying by 6, we have:

6n = 4n + 2n - n + 900

n = 900

Answer: E
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