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Question
If n(A ∪ B ∪ C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ∩ C) = 15, n(A ∩ C) = 25 and n(A ∩ B ∩ C) = 10, then the value of x is
Options
10
15
25
30
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Solution
15
Explanation;
Hint:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)
100 = 4x + 6x + 5x – 20 – 15 – 25 + 10
100 = 15x – 50
⇒ 150 = 15x
⇒ x = `150/15`
= 10
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