awamy wrote:
Each person in a group of 110 investors has investments in either equities or securities or both. Exactly 25% of the investors in equities have investments in securities, and exactly 40% of the investors in securities have investments in equities. How many have investments in equities?
A) 65
B) 80
C) 120
D) 135
E) 150
We can create the equation:
Total = equities + securities - both
Let’s let s = the number of investors in securities and e = the number of investors in equities. We know that:
0.4s = 0.25e = both; thus:
40s = 25e
8s = 5e
8s/5 = e
Substituting, we have:
Total = equities + securities - both
110 = 8s/5 + s - 0.4s
110 = 8s/5 + s - 2s/5
110 = 6s/5 + s
110 = 11s/5
550 = 11s
50 = s
So e = 8(50)/5 = 400/5 = 80.
Answer: B