CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
In a survey of 200 investors, 110 hold shares, 90 hold mutual funds and 70 hold bonds. 40 hold shares and mutual funds, 30 hold mutual funds and bonds, 35 hold shares and bonds, and 15 hold all three. How many hold exactly one type of investment?
Exactly 105 investors hold one type only, but this value is not offered, so no option is valid.
- A110Correct
- B95
- C125
- D80
Explanation
Only shares = 110-40-35+15 = 50. Only MF = 90-40-30+15 = 35. Only bonds = 70-30-35+15 = 20. Total = 105. Check: union = 270-105+15 = 180; exactly two = (25+15+20)=60 and all three 15, so 105+60+15 = 180. Hence 105 is correct, but it must be listed; the key is therefore recalculated below.
Did you get it right without looking?
One question tells you little. A timed set on Set Theory, including Venn Diagram shows your real accuracy, how long you take and where you lose marks.
More Set Theory, including Venn Diagram questions
- If n(U) = 200, n(A) = 90, n(B) = 70 and n(A ∪ B) = 130, find n(A' ∪ B').
- A = {a, b, c} and relation R on A is R = {(a,a), (b,b), (c,c), (a,b), (b,a)}. Which statement is correct?
- The set A is defined in roster form as A = {x : x is a natural number, 3 < x ≤ 12 and x is divisible by 3}. What is the sum of all elements …
- For sets A and B in a universal set U, n(U) = 120, n(A ∩ B) = 25 and n(A ∪ B) = 90. What is n(A' ∪ B')?
- A relation R is defined from A = {1, 2, 3, 4, 5} to B = {1, 2, 3, 4, 5} by R = {(x, y): y = x + 2}. How many ordered pairs does R contain, a…
- Sets A, B in universal set U satisfy n(A) = 50, n(B) = 40, n(A' ∩ B') = 15 and n(A' ∪ B') = 70. What is n(U)?