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

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

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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
[Reveal] Spoiler: OA

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

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New post 22 Jan 2017, 04:45
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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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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try table:
2/3=1/6 + 3/6
3/6+150=2/3
150=1/6 of attendeees
150*6=900
Answer is E

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

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New post 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

Therefore, answer is E.

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

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

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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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New post 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?

a) 300

b) 450

c) 600

d) 800

e) 900
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Re: How many attendees are at a convention if 150 of the attendees are [#permalink]

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New post 30 May 2017, 02:57
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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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


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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Re: How many attendees are at a convention if 150 of the attendees are   [#permalink] 01 Jun 2017, 10:13
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