If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

BTGModeratorVI wrote: ↑

Wed Dec 16, 2020 12:35 pm

If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

Answer: E
Source: Manhattan prep

----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.
-----------------------------

In this case we are told that n divided by 7 leaves a remainder of 2
So the possible values of n are: 2, 9, 16, 23, etc....

So let's say n equals 2
The question becomes "What is the remainder when 3 times 2 is divided by 7?"
In other words, "What is the remainder when 6 is divided by 7?"
7 divides into 6 zero times, leaving a remainder of 6

Answer: E


Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Dec 16, 2020 12:35 pm

If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

Answer: E

Solution:

We can let n = 2. Thus:

(3 x 2)/7 = 6/7 = 0 remainder 6.

Answer: E