When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

[BTGModeratorVI]

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

[dollydevashryee]

Easiest way to solve these questions is to plug in a number for x.
x = 8
8 % 20 = 8
8 % 5 = 3 -> B

[Brent@GMATPrepNow]

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

[Brent@GMATPrepNow]

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

Another approach:

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 positive integer x is divided by 20, the remainder is 8.
So, the possible values of x are: 8, 28, 48, 68, 88,...
Let's test a few values

8 divided by 5 equals 1 with remainder 3
28 divided by 5 equals 5 with remainder 3
48 divided by 5 equals 9 with remainder 3
68 divided by 5 equals 13 with remainder 3
88 divided by 5 equals 17 with remainder 3
.
.
.
It certainly LOOKS like the remainder will always be 3

Answer: B

Cheers,
Brent

[Scott@TargetTestPrep]

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