We can draw the following Venn diagram from the information given in the question.
Explanation:
From (1): a = 3g …(1)
From (2): c = (c + g) – 10 ⇒ g = 10 ⇒ a = 30 [From (1)]
From (3): e + f = a + b + 29 ⇒ e + f = 59 + b …(2)
From (4): a + e = 140 ⇒ 30 + e = 140 ⇒ e = 110
From (5): a + b = g + 100 ⇒ 30 + b = 10 + 100 ⇒ b = 80
⇒ e + f = 59 + b = 139 …(3) [From equation (2)] ⇒ 110 + f = 139 ⇒ f = 29
From (6): a + b + c + d + e = d + e + f + g + 86 ⇒ a + b + c = f + g + 86 ⇒ 30 + 80 + c = f + 10 + 86 ⇒ c = f - 14 ⇒ c = 15
Now, total number of people surveyed is 300. ∴ a + b + c + d + e + f + g = 300 ⇒ 30 + 80 + 15 + d + 110 + 29 + 10 = 300 ⇒ d = 26
∴ The final Venn diagram is:
∴ Number of people who subscribed for exactly one newspaper = c + g = 15 + 10 = 25.
Hence, 25.
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