gmattesttaker2 wrote:
Hello,
Can you please assist with this:
A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?
A) 18
B) 27
C) 36
D) 72
E) 180
OA:
I tried to solve using a Double Set Matrix:
------------------Male--------Female---------Total
Graduate 7x 2x 9x
Under Graduate - - (1/6)100
Total 30 70 100
Is it correct here to take the Total as 100 since it is mentioned that females constitute 70% of the group or should the total be an unknown x? Thanks for your help.
Regards,
Sri
Here is how you can use the double set matrix.
...................Male...............Female..............Total
Graduate .......7x..............
UnderGrad......2x......
Total.............9x
Female students make up 70% of the group and so male students make up 30% of the group.
9x = (30/100)*Total
Total = 30x (we got the total number of students in terms of x)
...................Male...............Female..............Total
Graduate .......7x................
UnderGrad......2x......
Total.............9x...................21x.................30x
Undergrad students make 1/6 of the group i.e. (1/6)*30x = 5x
...................Male...............Female..............Total
Graduate .......7x...................18x
UnderGrad......2x...................3x....................5x
Total.............9x...................21x.................30x
So undergrad females must be 3x and grad females must be 18x.
Number of Grad females must be a multiple of 18.
27 is not a multiple of 18 so it cannot be the number of grad females. Answer (B)