JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Sets Relations and Functions

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:

Answer: (D)

Solution

Using the principle of inclusion-exclusion for sets:

n (H \cup L) = n (H) + n (L) - n (H \cap L)

.

Since all patients have at least one ailment,

n (H \cup L) \leq 100

.

This gives:

89 + 98 - K \leq 100

, so

K \geq 87

.

Also,

K \leq min (89, 98) = 89

.

Therefore,

87 \leq K \leq 89

.

The set

{79, 81, 83, 85}

contains values less than 87, so K cannot belong to this set.

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Single correct option