Convention prob

[AIM TO CRACK GMAT]

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?

Options

a)300 b)450 c)600 d)800 e)900

ill b glad if sum1 could help me asap

[aman88]

IMO E.

*these type of problems will sound very easy if you can make a grid and interpret the values in the grid.

[sharoonsaleem]

Aman is so right. Make a grid and these questions will come in easy peesy

[Brent@GMATPrepNow]

I thought I'd point out that the "grid" technique that others are referring to is also known as the Double Matrix Method. It can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- gender (female or male)
- schooling status (student or non-student)

For more information about this technique and some additional practice questions, check out these 3 BTG articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

[GMATGuruNY]

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?

Options

a)300 b)450 c)600 d)800 e)900

ill b glad if sum1 could help me asap

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.

[vishugogo]

Students Not students Total

Female x/6 x/2 2x/3

Not Female x/6 150 150+x/6

Total x/3 150+x/2 x

use options

Option E.....get the equation correct