BTGModeratorVI wrote: ↑Sun Mar 15, 2020 12:42 pm
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3n
II. 5n
III. 4n + 10
A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III
Answer:
B
Source: Princeton Review
Many integer properties questions can be solved by
testing values
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.
When integer n is divided by 15, the remainder is 5.
So, some possible values of n are: 5, 20, 35, 50, 65, ....
Which of the following has a remainder of 10 when divided by 15 ?
Let's test a possible value of n.
Try n = 5
I. 3n = 3(
5) = 15. When we divide 15 by 15, we get remainder 0. So, statement I does NOT satisfy the requirement.
ELIMINATE answer choices A, D and E
II. 5n = 5(
5) = 25. When we divide 25 by 15, we get remainder 10. So, statement II DOES satisfy the requirement. This means we can't eliminate anything.
III. 4n + 10 = 4(
5) + 10 = 30. When we divide 30 by 15, we get remainder 0. So, statement III does NOT satisfy the requirement.
ELIMINATE answer choice C
Answer: B
