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

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Math Expert
Joined: 02 Sep 2009
Posts: 55609
How many attendees are at a convention if 150 of the attendees are  [#permalink]

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22 Jan 2017, 04:13
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Difficulty:

45% (medium)

Question Stats:

72% (02:34) correct 28% (02:57) wrong based on 407 sessions

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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?

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

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Math Expert
Joined: 02 Sep 2009
Posts: 55609
Re: How many attendees are at a convention if 150 of the attendees are  [#permalink]

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15 Apr 2017, 10:03
1
5
ehsan090 wrote:
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

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

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22 Jan 2017, 04:45
2
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

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

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22 Jan 2017, 05:47
2
1
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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11 Mar 2017, 14:01
1
try table:
2/3=1/6 + 3/6
3/6+150=2/3
150=1/6 of attendeees
150*6=900
Manager
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Posts: 243
Re: How many attendees are at a convention if 150 of the attendees are  [#permalink]

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11 Mar 2017, 20:37
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

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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
1
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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Got Q42,V17
Target#01 Q45,V20--April End
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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, 23:01
Bunuel wrote:
ehsan090 wrote:
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

Hope it helps.

Thanks Bunuel you are always of Great help!!
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Re: How many attendees are at a convention if 150 of the attendees are  [#permalink]

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01 Jun 2017, 10:13
1
1
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

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

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

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25 Dec 2018, 11:13
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Re: How many attendees are at a convention if 150 of the attendees are   [#permalink] 25 Dec 2018, 11:13
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