Question

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?

Answer 1

dividend = (integer quotient)*(divisor) + remainder 
n = 3p + 2 
n = 5q + 1

where p and q are the quotients.

Now, we can plug in the values of p and q into the equations, starting with 0:

n = 3p + 2 
p = 0 --> n = 3*0 + 2 = 2 
p = 1 --> n = 3*1 + 2 = 5 
p = 3 --> n = 3*2 + 2 = 8 
p = 4 --> n = 3*3 + 2 = 11 
etc.

n = 5q + 1 
q = 0 --> n = 5*0 + 1 = 1 
q = 1 --> n = 5*1 + 1 = 6 
q = 2 --> n = 5*2 + 1 = 11

We can stop here, since we have found a common value for n, n = 11. Therefore, the least possible value for n for which both statements is true is n = 11 :)

Hope this helps!