Problem Solving

AndrewRivera7793 wrote:When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

A) 11
B) 9
C) 7
D) 6
E) 4

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.

Here, we are told that n divided by 45 leaves a remainder of 18, so the possible values of n are: 18, 63, 108,... etc.

IMPORTANT: the question asks, "Which of the following must be a divisor of n?
So, let's test the smallest possible value of n, which is 18, and check the answer choices.

18 is NOT divisible by 11, 7 or 4, so we can ELIMINATE A, C and E.
So, the correct answer is either B or D

Now test the next possible value of n, which is 63.
63 is NOT divisible by 6, so we can ELIMINATE D

So, by the process of elimination, the correct answer is B

Cheers,
Brent

AndrewRivera7793 wrote:When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

A) 11

B) 9

C) 7

D) 6

E) 4

We can find all possible values of n by adding the remainder 18 to integer multiples of 45. Thus, we see that n can be values such as 18 or 63 or 108.

The only common factors of these three numbers are 1 and 9. Since 1 is not in the answer choices, the correct answer must be 9.

Answer: B