sandy 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
Practice Questions
Question: 10
Page: 62
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
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