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

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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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