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

Question

How many attendees are at a convention if 150 of the attendees are neither female nor students, one-sixth of the attendees are female students, two-thirds of the attendees are female, and one-third of the attendees are students?

A. 300
B. 450
C. 600
D. 800
E. 900

A. 300 
B. 450 
C. 600 
D. 800 
E. 900

Bunuel · Accepted Answer

Overlapping Sets Made Easy!   
   ADVANCED OVERLAPPING SETS PROBLEMS   
   How to draw a Venn Diagram  
   Data Sufficiency Questions on Overlapping Sets  
   Problem Solving Questions on Overlapping Sets

Hope it helps.

Nightfury14 · Answer

Let x be the total number of attendees

___________| Student__| Not-student |____  
 Female ____|__x/6____|__________| 2x/3  
 Not-Female_|_________|____150___|_____ 
 ___________|__x/3____|__________| X

Now  \frac{x}{6}  (Not Female Student) + 150 =  \frac{x}{3}  (Not Female Attendees)
  \frac{x}{6}  = 150
x = 900

RMD007 · Answer

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.

SeregaP · Answer

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

matthewsmith_89 · Answer

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.

ehsan090 · Answer

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

ehsan090 · Answer

Thanks  Bunuel  you are always of Great help!!

ScottTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards