When positive integer n is divided by 3, the remainder is 2 and when

When positive integer n is divided by 3, the remainder is 2 and when positive integer t is divided by 5 the remainder is 3. What is the remainder when the product nt is divided by 15?

1. n-2 is divisible by 5
2. t is divisible by 3

Known from Q stem: n = 3k + 2; t = 5p + 3
Is this rephrasing correct? nt = 15kp + 9k + 10p + 6

Statement 1 tells us that:
(3k+2)-2 = an integer. (3k)/5. Thus, k must be a multiple of 5
5

Statement 2 tells us that:
5p+3 = an integer or (5/3)p +1 is an integer. Thus, p must be a multiple of 3
3

Going back to your original rephrase:
nt = 15kp + 9k + 10p + 6

rewrite as, what is the remainder of:
(15kp) + (3^2*k) + (2*5*p) + (6)
15

break down the four parts:
15kp/15 has no remainder
(3^2)*k/15 has no remainder because k is a multiple of 5
2*5*p/15 has no remainder because p is a multiple of 3
6 will always be the remainder and your answer is C

Number Plugging also works……….