List of top Quantitative Ability and Data Interpretation Questions on Divisibility Rules asked in XAT

The addition of 7 distinct positive integers is 1740. What is the largest possible “greatest common divisor” of these 7 distinct positive integers?

Let X be a four digit number with exactly three consecutive digits being the same, and X is a multiple of 9. How many such X's are possible?

S is a set of five-digit numbers formed using the natural numbers between 2 and 8 exactly once. How many numbers of set S are divisible by 11?