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One-sixth of the attendees at a certain convention are femal

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by BTGmoderatorDC » Mon Feb 18, 2019 9:54 pm

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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

OA E

Source: Manhattan Prep
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Source: — Problem Solving |

by Jay@ManhattanReview » Mon Feb 18, 2019 10:54 pm
BTGmoderatorDC wrote: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

OA E

Source: Manhattan Prep
Already replied two days back...

https://www.beatthegmat.com/one-sixth-o ... tml#827021

Hope this helps!

-Jay
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Manhattan Review GMAT Prep

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by Scott@TargetTestPrep » Thu Feb 21, 2019 4:53 pm
BTGmoderatorDC wrote: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

OA E

Source: Manhattan Prep
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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