One-sixth of the attendees at a certain convention are

BTGmoderatorLU wrote:Source: Manhattan Prep

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

The OA is E

See the image below, which is self-explanatory.



The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Manhattan Prep

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

The OA is E

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