Question

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments, then $K$ can not belong to the set:

• A. $\{84,87,90,93\}$
• B. $\{84,86,88,90\}$
• C. $\{79,81,83,85\}$
• D. $\{80,83,86,89\}$

Answer 1

The correct option is C $\{79,81,83,85\}$

Let $A$ denotes the set of patients suffering from heart ailment and $B$ denotes the set patients suffering from lungs infection.

$n\left(A\right)=89,n\left(B\right)=98\text{and}n(A\cap B)=K$
$\because n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$\Rightarrow 89+98-K\le 100$
$\Rightarrow K\ge 87$