2016 · Q6
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1,2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A ?
Elementary MathematicsNumber System
- ANo integer
- BOne
- CTwo
- DThree
Explanation
Remainders 1,2,3,4,5 on division by 2,3,4,5,6 mean each number is one less than a common multiple of 2,3,4,5,6. Since lcm(2,3,4,5,6) = 60, the numbers are of the form 60k−1. Between 0 and 100 only k = 1 works, giving 59 — exactly one integer (option B).