## When positive integer x is divided by 20, the remainder is 8

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### When positive integer x is divided by 20, the remainder is 8

by BTGmoderatorLU » Wed Mar 14, 2018 3:04 pm
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

The OA is B.

I get the solution to this PS question as follow,

When x is divided by 20 the remainder is 8.

Therefore x is of form 20k + 8, where k is an integer.

When x is divided by 5, the component 5(4k + 1) is divided by 5. Hence, remainder when x is divided by 5 = remainder(3/5) = 3. Option B.

Experts, any suggestion? Thanks in advance.

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by [email protected] » Wed Mar 14, 2018 3:19 pm
LUANDATO wrote: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
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

Cheers,
Brent
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by [email protected] » Fri Mar 16, 2018 7:50 am
LUANDATO wrote: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

The OA is B.

I get the solution to this PS question as follow,

When x is divided by 20 the remainder is 8.

Therefore x is of form 20k + 8, where k is an integer.

When x is divided by 5, the component 5(4k + 1) is divided by 5. Hence, remainder when x is divided by 5 = remainder(3/5) = 3. Option B.

Experts, any suggestion? Thanks in advance.
Note that in these types of questions, x can always equal the remainder. (8/20 is the same thing as 0 + 8/20.) You can see this if you take Brent's equation and plug 0 into the Q.
If x = 8, then 8/5 = 1 + 3/5, giving us a remainder of 3. The answer is B
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by [email protected] » Fri Mar 16, 2018 10:42 am
Hi LUANDATO,

DavidG brings up a good point - when TESTing VALUES in these types of questions, the easiest value for X is almost always the remainder itself. That having been said, you don't have to use that value to get the correct answer. If we use X = 28, then 28/20 = 1 r 8.... and the answer to the question is 28/5 = 5 r 3 --> so the answer is still 3.

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by [email protected] » Mon Mar 19, 2018 3:31 pm
LUANDATO wrote: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
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.

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by deloitte247 » Thu Mar 29, 2018 1:54 pm
$$\frac{x}{20}=Q+\frac{8}{20}$$
$$x=20Q+8$$
$$when\ x\ is\ divided\ by\ 5\ i.e\ \frac{x}{5}=???$$
$$substituting\ 20Q+8=x$$
$$we\ have,\ \frac{\left(20Q+8\right)}{5}=4Q+\frac{8}{5}$$
$$=4Q+1\frac{3}{5}$$
$$Hence,\ the\ remainder\ is\ 3.\ Option\ B$$

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