Problem Solving

If the number 52,1n9, where n represents the tens digit, is a multiple of 3, then the value
of n could be which of the following?
A. 6
B. 5
C. 3
D. 1
E. 0

is the answer "D" ?

Quick trick for deciding if a number is a multiple of 3:

if the sum of the digits of the number is a multiple of 3, then the whole number is a multiple of 3.

Here we have:

52,1n9 and know that the number is a multipe of 3.

Therefore, 5+2+1+n+9 = a multiple of 3

17 + n = a multiple of 3.

Looking at the choices, only

(d) 1

will give us what we want (since 17+1=18, which is a multipe of 3).

Here is a great link for divisibility rules:

https://www.mathwarehouse.com/arithmetic ... -tests.php

It has 2,3,4,5,6,7,8,10, and 11

Again Backsolving helps

I also used backsolving, but knowing the divisibility rule would have been much faster. I would've used the divisibility rule if I didn't doubt myself due to 9 having the same divisibility rule.