List of top Quantitative Ability and Data Interpretation Questions on LCM and HCF asked in XAT

A chose an integer X, which is between 2 and 40. A noticed that X is such a number that, when any integer Y is divided by X, the remainder is always 1. What is the value of X?

Find the least number which when divided by 35, 45, and 55 leaves the remainder 18, 28, and 38 respectively.