List of top Quantitative Ability Questions on Number System asked in XAT

The sum of the numbers from 1 to 100, which are not divisible by 3 and 5.

If \(n\) is a positive integer, let \(S(n)\) denote the sum of the positive divisors of \(n\), including \(n\) itself, and let \(G(n)\) be the greatest divisor of \(n\). If \(H(n) = \dfrac{G(n)}{S(n)}\), then which of the following is the largest?

For \(n = 1, 2, 3, \ldots\), let \(T_n = 1^3 + 2^3 + \cdots + n^3\). Which one of the following statements is correct?
How many numbers between 1 and 1000 (both excluded) are both squares and cubes?