Problem Solving

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

Correct me if I am mistaken, but I think the OA is E, 900.

Anurag@Gurome wrote:

AIM TO CRACK GMAT 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?

Let us plug the answer,

Option A : 300 = Total number of attendees.
Hence, number of female students = 1/6 of 300 = 50

Number of attendees who are not student = 2/3 of 300 = 200

Hence, number of attendees who are neither female nor students = (200 - 50) = 150 --> SUCCESS

The correct answer is A.

i am really sorry....i loved ur method but the answer is E here...ill b glad if u cud teme hw its possible?

purple3594 wrote:Correct me if I am mistaken, but I think the OA is E, 900.

Yes u r right... ill b glad if u cud teme a simpler way to get the right answer jus like hw anurag did... HW did u get it?

I think your answer is incorrect Anurag.

If 1/3 of all attendees are students, and 2/3 of all attendees are female, we essentially need to find the part that does not lie in the intersection between these two sets, i.e. male non-students.

So, if 2/3 are female, that means our answer has to be less than or equal to 1/3. Of the 1/3 that are students, half are female and half are male. So essentially 1/6 of the total attendees are female students and 1/6 are male students. Now, we know that 1/3 of all attendees are male (1 - 2/3 female attendees). If 1/6 of all attendees are male students, that means you have to subtract 1/6 from 1/3 (male attendees) to find all male non-students. That leaves us with 1/6 of all attendees being male non-students.

Since this represents 150, the total attendee list should be 6*150 or 900.

AIM TO CRACK GMAT 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 can solve using a matrix since we have two variables: female/male and student/nonstudent. Everything in blue is what we know up front:

Nonstudent and male = 150
Student and female = 1/6 of total
Female (student AND nonstudent) = 2/3 of total
Student (female AND male) = 1/3 of total

If we combine the middle two statements, we can find the the nonstudent and female group, where a is the total number of attendees and x is the female nonstudent group:

a/6 + x = 2a/3
a/6 + x = 4a/6
x = 3a/6 = a/2

Female nonstudents must be half of the total

We can now use that value (female nonstudents) with our knowledge of male nonstudents to find the total number of attendees (which we'll call a):

a/2 + 150 = 2a/3
3a/6 + 150 = 4a/6
150 = a/6

900 = a

AIM TO CRACK GMAT 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

An alternate approach is to use the following formula:

Total = Group 1 + Group 2 - Both + Neither.

The big idea with overlapping groups is the SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (females) and everyone in Group 2 (students), those in BOTH groups (female students) are counted TWICE.
Thus, we SUBTRACT THE OVERLAP -- the number in both groups -- so that these people are not double-counted.

Since the LCM of the denominators in the problem is 6, let the total = 6x.
Group 1 = females = (2/3)6x = 4x.
Group 2 = students = (1/3)6x = 2x.
Both = female students = (1/6)6x = x.
Neither = 150.

Plugging these values into the formula, we get:
6x = 4x + 2x - x + 150
x = 150.

Thus, the total number of attendees = 6x = 6(150) = 900.

The correct answer is E.

Bill@VeritasPrep wrote:

AIM TO CRACK GMAT 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 can solve using a matrix since we have two variables: female/male and student/nonstudent. Everything in blue is what we know up front:

Nonstudent and male = 150
Student and female = 1/6 of total




Female (student AND nonstudent) = 2/3 of total
Student (female AND male) = 1/3 of total

If we combine the middle two statements, we can find the the nonstudent and female group, where a is the total number of attendees and x is the female nonstudent group:

a/6 + x = 2a/3
a/6 + x = 4a/6
x = 3a/6 = a/2

Female nonstudents must be half of the total

We can now use that value (female nonstudents) with our knowledge of male nonstudents to find the total number of attendees (which we'll call a):

a/2 + 150 = 2a/3
3a/6 + 150 = 4a/6
150 = a/6

900 = a

Thanks 4 d help... Appreciate it alot!! its easier this way!!