Question

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,

• A. Only (a) and (b) are correct
• B. Only (a) and (c) are correct
• C. Only (b) and (c) are correct
• D. All (a), (b) and (c) are correct

Answer 1

Answer: (D)

All (a), (b) and (c) are correct

Answer 2

$n(P) = 25$
$n(C)= 15$
$n\left(P' \cup C'\right) = 65\%$
$\Rightarrow n\left(P \cup C\right)' = 65\%$
$n\left(P\cup C\right) = 35\%$
$n\left(P\cap C\right) = n\left(P\right) + n\left(C\right)-n\left(P\cup C\right)$
$25+15-35 = 5\%$
$x \times 5\% = 2000$
$x=40,000$