How many attendees are at a convention if 150 of the attendees are

Let total attendees be x.

Total Female attendees = 2x/3; Female Students = x/6; So Females which are not student are = x/2;
Total Attendees x; Total students = x/3; So Non students = 2x/3;

Females which are not students + Attendees which are neither females nor students = Total attendees which are not student.
x/2+150 = 2x/3;
x= 900

E.

try table:
2/3=1/6 + 3/6
3/6+150=2/3
150=1/6 of attendeees
150*6=900
Answer is E

I did it this way and got the answer

P(FUS) = P(F) + P(S) - P(FNS)
x - 150 = 2/3x + 1/3x - 1/6x
x - 150 = 5/6x
x = 150(6)
x = 900

Therefore, answer is E.

can anyone guide me from where should i go through concept of this question
I need basic foundation struggling in these type of questions
TIA

Thanks Bunuel you are always of Great help!!

We will use the overlapping sets formula, which is:

#(attendees) = #(female) + #(student) - #(both female and student) + #(neither female nor student).

Let’s denote the total number of attendees by x, i.e., #(attendees) = x.

Since 150 of the attendees are neither female nor student, #(neither female nor student) = 150.

Since 1/6 of the attendees are female students, #(both female and student) = (1/6)x.

Since 2/3 of the attendees are female, #(female) = (2/3)x.

Since 1/3 of the attendees are students, #(students) = (1/3)x.

Let’s plug in each of the above into the formula:

x = (2/3)x + (1/3)x - (1/6)x + 150

x = x - (1/6)x + 150

(1/6)x = 150

x = 900

Answer: E

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