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Maths-

General

Easy

Question

A survey shows that 63% of the Americans like cheese whereas 76% like apples. If $x$ % of the Americans like both cheese and apples, then

$x = 39$
$x = 63$
$39 \leq x \leq 63$
None of these

The correct answer is: $39 less or equal than x less or equal than 63$

Given, $n open parentheses C close parentheses equals 63 comma blank n open parentheses A close parentheses equals 76$ and $n open parentheses C intersection A close parentheses equals x$
We know that,
$n open parentheses C union A close parentheses equals n open parentheses C close parentheses plus n open parentheses A close parentheses minus n left parenthesis C intersection A right parenthesis$
$rightwards double arrow blank 100 equals 63 plus 76 minus x rightwards double arrow x equals 139 minus 100 equals 39$
And $n left parenthesis C intersection A right parenthesis less or equal than n left parenthesis C right parenthesis$
$rightwards double arrow blank x less or equal than 63 blank$
$therefore 39 less or equal than x less or equal than 63$

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