Question

N and t are both positive integers. If n-3 can be divided by 5 and t can be divided by 2, what is the remainder when the product of n and t is divided by 10

Answer 1

Excellent question! Yes, we can derive a general formula to approach this question :) First, use the statements to write two equations in the form

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!