CAT Exam 2021 Slot 1 Solved Paper

We have
Now, the difference inside the modulus signified the distance of n from $60,100,\mathrm{and}20$ on the number line. This means that when the absolute difference from a number is larger, n would be further away from that number.
Example: The absolute difference of n and 60 is less than that of the absolute difference between n and 20. Hence, n cannot be , as then it would be closer to 20 than 60, and closer on the number line would indicate lesser value of absolute difference. Thus we have the condition that $\mathit{n}>40$
The absolute difference of n and 100 is less than that of the absolute difference between $\mathit{n}\mathrm{and}20$ Hence, n cannot be , as then it would be closer to 20 than 100. Thus we have the condition that $\mathit{n}>60$
The absolute difference of n and 60 is less than that of the absolute difference between $\mathit{n}\mathrm{and}100$ Hence, n cannot be , as then it would be closer to 100 than 60. Thus we have the condition that
The number which satisfies the conditions are 61, 62, 63, 64......79. Thus, a total of 19 numbers.
Alternatively
as per the given condition :
Dividing the range of n into 4 segments. $(n < 20, 20 100)$
1) For
$\left|\mathit{n}-20\right|=20-\mathit{n},|\mathit{n}-60|=60-\mathit{n},|\mathit{n}-100|=100-\mathit{n}$
considering the inequality part :

No value of n satisfies this condition.
2) For
$\left|\mathit{n}-20\right|=\mathit{n}-20,|\mathit{n}-60|=60-\mathit{n},|\mathit{n}-100|=100-\mathit{n}$

For
But for the considered range n is less than 60.
3) For
$\left|\mathit{n}-20\right|=\mathit{n}-20,|\mathit{n}-60|=\mathit{n}-60,|\mathit{n}-100|=100-\mathit{n}$

For the first part and for the second part
n takes values from 61 ................79.
A total of 19 values
4) For $\mathit{n}>100$
$\left|\mathit{n}-20\right|=\mathit{n}-20,|\mathit{n}-60|=\mathit{n}-60,|\mathit{n}-100|=\mathit{n}-100$

No value of n in the given range satisfies the given inequality.
Hence a total of 19 values satisfy the inequality.