CAT 2003 Slot 2 — QA Question 23

$\left(1-\frac{1}{n}\right)<x\le \left(3+\frac{1}{n}\right),$ wher n is a positive integer

If n = 1, then 0 < x ≤ 4

As the value of n increases from 1 to infinity, the range of x approaches (1 < x ≤ 3).

So, the lower limit of x increases from almost 0 (to almost 1), while the higher limit decreases from 4 (to 3).

Thus, the lowest possible limit of x will be > 0 and the highest possible limit will be ≤ 4.

∴ For all range of n, 0 < x ≤ 4

Hence, option (c).