Aspire Faculty ID #16291 · Topic: NIMCET 2010 · Just now
NIMCET 2010

Survey: $63%$ like cheese, $76%$ like apples. If $x%$ like both?

Solution

Using inclusion–exclusion: 
$63 + 76 - x \le 100$ 
$139 - x \le 100$ 
$x \ge 39$ 
 Max value of $x$ cannot exceed minimum of both percentages 
→ $x \le 63$ 
 Thus $39 \le x \le 63$.
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