# Math Help - venn diagram

1. ## venn diagram

In a college, 60% of all sophomores have liberal studies as their major subject, 24% of all sophomores have social history as their major and the rest have other subjects or have not yet chosen a major. If 55% of all sophomores have chosen psychology as a course, then what is the minimum percent of all sophomores who have chosen psychology as a course and who also have liberal studies as their major subject?

my answer is 15 is it correct

2. Originally Posted by arunachalam.s
In a college, 60% of all sophomores have liberal studies as their major subject, 24% of all sophomores have social history as their major and the rest have other subjects or have not yet chosen a major. If 55% of all sophomores have chosen psychology as a course, then what is the minimum percent of all sophomores who have chosen psychology as a course and who also have liberal studies as their major subject?

my answer is 15 is it correct
I prefer using a Karnaugh table:

$\begin{tabular}{l | c | c | c | c} & Liberal & Social history & Other & \\ \hline Psychology & x & a & b & 0.55\\ \hline Not Psychology & c & d & e & 0.45 \\ \hline & 0.6 & 0.24 & 0.16 & 1 \\ \end{tabular}
$

Your task is to find the smallest possible value of x. You have the following equations:

x + a + b = 0.55 .... (1)

x + c = 0.6 .... (2)

c + d + e = 0.45 .... (3)

b + e = 0.16 .... (4)

a + d = 0.24 .... (5)

and you want the smallest value of x for which these equations will be consistent.

So I get x = 0.15 which is equivalent to 15% so yes you're correct.

(No doubt someone will give a simple two line confirmation of this).

3. what is the relevance of the 24 % figure ... probably u r missing some info

4. Originally Posted by nirax
what is the relevance of the 24 % figure ... probably u r missing some info
The question is fine as it is. That should be clear from what I posted ealier. A minimum possible value of x is required, not the value.

5. if all you are concerned with is liberal studies and psychology then social history is an irrelevant info ... even if that figure were 100%, your desired answer would not change.

thats what led me to suspect that you r missing something