CAT 2022 Slot 1 QA Question 12: The average of three integers is $13$. When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$ is

Question

The average of three integers is $13$. When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$ is

Accepted Answer

Sum of the three integers = $3 	imes 13 = 39$
After including $n$, the new average is
$\dfrac{39+n}{4}$
This must be an odd integer. The smallest possible odd integer average greater than or equal to $10$ is $11$.
$\dfrac{39+n}{4} = 11$
$\Rightarrow 39+n = 44$
$\Rightarrow n = 5$
Answer: (2) 5

The average of three integers is 131313. When a natural number nnn is included, the average of these four integers remains an odd integer. The minimum possible value of nnn is

The average of three integers is $13$ . When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$ is