CAT 2003 Slot 1 — QA Question 38

The first layer has 1 ball.

Second layer has 1 + 2 = 3 balls

Third layer has 1 + 2 + 3 = 6 balls

∴ The nth layer of the stack would have $\left[\frac{n(n+1)}{2}\right]$ balls

∴ Total balls in all the layers = $\sum _{}^{}\left[\frac{n(n+1)}{2}\right]$ = 8436

∴ $\frac{1}{2}\times \left[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}\right]$ = 8436

Only n = 36 satisfies the above equation.

Hence, option (c).