Out of all the patients in a hospital 89% are found to be suffering
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 $\mathrm{K} \%$ of them are suffering from both ailments, then $\mathrm{K}$ can not belong to the set :

1. $\{80,83,86,89\}$

2. $\{84,86,88,90\}$

3. $\{79,81,83,85\}$

4. $\{84,87,90,93\}$

Correct Option: 3,

Solution:

$\mathrm{n}(\mathrm{A} \cup \mathrm{B}) \geq \mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})-\mathrm{n}(\mathrm{A} \cap \mathrm{B})$

$100 \geq 89+98-n(A \cup B)$

$\mathrm{n}(\mathrm{A} \cup \mathrm{B}) \geq 87$

$87 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 89$

Option (3)