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Re: When positive integer x is divided by 20, the remainder is 8. What is
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12 Jul 2021, 08:25
Carcass 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
Re: When positive integer x is divided by 20, the remainder is 8. What is
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22 Jul 2024, 18:00
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Re: When positive integer x is divided by 20, the remainder is 8. What is [#permalink]