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
One-sixth of the attendees at a certain convention are
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See the image below, which is self-explanatory.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
The correct answer: E
Hope this helps!
-Jay
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We can create the following equation: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
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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