JEE PYQ: Sets And Relations Question 8
Question 8 - 2020 (04 Sep Shift 1)
A survey shows that 63% of the people in a city read newspaper $A$ whereas 76% read newspaper $B$. If $x$% of the people read both the newspapers, then a possible value of $x$ can be:
(1) 29
(2) 37
(3) 65
(4) 55
Show Answer
Answer: (4)
Solution
Let $n(U) = 100$, then $n(A) = 63$, $n(B) = 76$
Now, $n(A \cup B) = n(A) + n(B) - n(A \cap B) \leq 100$
$= 63 + 76 - x \leq 100$
$\Rightarrow x \geq 139 - 100 \Rightarrow x \geq 39$
$\because n(A \cap B) \leq n(A)$
$\Rightarrow x \leq 63$
$\therefore 39 \leq x \leq 63$
BETA
