Problem Solving

M7MBA wrote:1. When n divided by 3, the remainder is 2.
2. When n divided by 4, the remainder is 1
3. What is the remainder when divided by 12?

A 1
B 3
C 4
D 5
B 12

IMPORTANT: Many integer property questions can be found quickly by identifying values that satisfy the given information.

---------ASIDE------------------
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.
---------ONTO THE QUESTION!-------------------------

1) When n divided by 3, the remainder is 2.
So, some possible values of n are: 2, 5, 8, 11, 14, 17, 20, . . . etc

2) When n divided by 4, the remainder is 1
So, some possible values of n are: 1, 5, 9, 13, 17, 21, . . . etc

As you can see, I listed more numbers than are necessary. We already have TWO values (n = 5, and n = 17 ) that satisfy both conditions.

What is the remainder when divided by 12?
If n = 5, then 5 divided by 12 equals 0 with remainder 5
So, the correct answer is D

If we had chosen a different possible value for n, the answer would be the same.
For example, if n = 17, then 17 divided by 12 equals 1 with remainder 5
So, the correct answer is still D

Cheers,
Brent