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

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

by BTGmoderatorDC » Thu Jan 19, 2023 3:58 am

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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

OA B

Source: Veritas Prep

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

by [email protected] » Thu Jan 19, 2023 6:53 am
BTGmoderatorDC wrote:
Thu Jan 19, 2023 3:58 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

OA 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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

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

by [email protected] » Fri Jan 20, 2023 7:39 am
BTGmoderatorDC wrote:
Thu Jan 19, 2023 3:58 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

OA B

Source: Veritas Prep
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.