school caffe

[agma]

Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussel sprouts. Of these students, 2/3 dislikes lima beans; and of thsoe who dislike lima beans, 3/5 also dislikes brussels sprouts. How many of student like brussels sprouts but dislike lima beans?


1) 120 students eat in the cafe.
2) 40 of the students like lima beans.

The answer provided is each sufficient.

My answer 1 and 2 togeather insufficient.
Why
How many likes brussels sprouts is not provided.
3/5 is the students who likes lima beans but not brussels sprouts.
There could be some common population who neither likes lima beans nor likes brussels sprouts?

[powerthelogic]

total students = x .
let us take like this .
no. of students who like only Lima Beans = a
no. of students who like only brussel sprouts = c
no. of students who like both Lima & Brussel = b
no of students who doesnot like both = d .
x = a+b+c+d .

from question::
dislike lima beans = 2/3*x = c+d .
3/5*2/3*x = 2/5*x = d
like brussel but dislike lima = c =?
c = 2/3 - 2/5 = 4/15*x .

so we need to know x ( total no. of students) .
from (1) x = 120 . yes we can answer.
from (2) 40 = a+b = 1/3*x , we can get x .

so each statement alone is sufficent.

D .

[powerthelogic]

the explaination might sound hard. it is good to explain in venn diagrams rather than equations.