Carcass wrote:
When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n?
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
GIVEN: When the positive integer n is divided by 3, the remainder is 2
The possible values of n are: 2, 5, 8,
11, 14, 17, 20,...
GIVEN: When n is divided by 5, the remainder is 1
The possible values of n are: 1, 6,
11, 16, 21,...
11 is the smallest value that appears in both lists of possible n-values.
Answer: 11
Cheers,
Brent