BTGModeratorVI wrote: ↑Mon Jun 08, 2020 11:57 am
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?
A. 1
B. 3
C. 5
D. 8
E. Cannot be determined
Answer:
B
Source: Veritas Prep
There's a nice rule that say, "
If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
In this case, we aren't told how many times 20 divides into x, but this isn't a problem.
Let's just say that 20 divides into x k times.
In other words,
x divided by 20 equals k with remainder 8
Applying the above
rule, we can then say: x = 20k + 8 for some positive integer k
What is the remainder when x is divided by 5?
We know that: x = 20k + 8
Rewrite as: x =
20k + 5 +
3
And the factor to get: x =
5(4k + 1) +
3
So, we can see that
x is 3 greater than some multiple of 5
This tells us that, if we divide x by
5, the remainder will be
3
Answer: B
Cheers,
Brent
