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

Say n = 20 + 8 = 28

We see that 28 divided by 5 has a remainder 3.

The correct answer: B

Hope this helps!

-Jay
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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

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

Solution:

We can create the equation:

x/20 = Q + 8/20

x = 20Q + 8

When 20Q + 8 is divided by 5 we have:

(20Q + 8)/5 = 4Q + 8/5

Since 8/5 = 1 3/5, the remainder is 3.

Alternate Solution:

Since we have a remainder of 8 when x is divided by 20, x could equal 28. When we divide 28 by 5, the quotient is 5 with a remainder of 3.

Answer: B