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:

Step-by-step solution

n C = 73 ,   n T = 65 ,   n C ∩ T = x , Considering that value of n C ∪ T cannot exceed 100 in terms of percentage, we get n C ∪ T ≤ 100 ⇒    n C + n T - n C ∩ T ≤ 100 ⇒    x ≥ 38 Therefore, x ≠ 36 . n C ∩ T ≤ min n C , n T   ⇒   x ≤ 65 ⇒   38 ≤ x ≤ 65 Hence x may assume values 63 , 54 , 38 .