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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?

Re: How many attendees are at a convention if 150 of the attendees are [#permalink]

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22 Jan 2017, 04:45

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Bunuel wrote:

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

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

Re: How many attendees are at a convention if 150 of the attendees are [#permalink]

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22 Jan 2017, 05:47

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Bunuel wrote:

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

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
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Re: How many attendees are at a convention if 150 of the attendees are [#permalink]

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15 Apr 2017, 09:59

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
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How many attendees are at a convention if 150 of the attendees [#permalink]

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30 May 2017, 02:28

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?

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

Merging topics. Please refer tot he discussion above.

Also, please search before posting. Thank you.
_________________

Re: How many attendees are at a convention if 150 of the attendees are [#permalink]

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30 May 2017, 09:19

Bunuel wrote:

mbaaspirant80 wrote:

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

Merging topics. Please refer tot he discussion above.

Also, please search before posting. Thank you.

Hi Bunnel, Thank you very much. I searched before posting and I find one thread of GMATClub which was closed.
_________________

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

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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