A survey shows that 73% of the persons working in an office like coffee, whereas 65% like …

Question

A survey shows that 73\% of the persons working in an office like coffee, whereas 65\% like tea. If $x$ denotes the percentage of them who like both coffee and tea, then $x$ cannot be:

Accepted Answer

C $$ \to $$ person like coffee

T $$ \to $$ person like Tea

n(C) = 73

n(T) = 65

n(C $$ \cup $$ T) $$ \le $$ 100

n(C) + n(T) -- n (C $$ \cap $$ T) $$ \le $$ 100

73 + 65 -- x $$ \le $$ 100

x $$ \ge $$ 38

73 -- x $$ \ge $$ 0 $$ \Rightarrow $$ x $$ \le $$ 73

65 -- x $$ \ge $$ 0 $$ \Rightarrow $$ x $$ \le $$ 65

$$ \therefore $$ 38 $$ \le $$ x $$ \le $$ 65

Solutions · 1