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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:

(1) 63

(2) 38

(3) 54

(4) 36
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Note**then x cannot be:

C > person like coffee

T > Person like Tea

n(C)=73

n(T) =65

n(C U T) $$≤$$ 100

n(C)+n(T) -n(C ∩ T) ≤ 100

73+65-x ≤ 100

x≥ 38

73-x ≥0 ⇒ x ≤ 73

65-x ≥0 ⇒x ≤65

38≤x≤ 65

Excluding 36 all options is in between 38≤x≤ 65  hence 36 is correct option

by Expert (11.5k points)