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22 Oct 2023, 16:10
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E
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Difficulty:
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Question Stats:
62% (01:51) correct
38%
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wrong
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If n is a negative integer and q is a positive integer, then there is only one negative integer m such that n = mq + r, where 0 ≤ r ≤ q. The Integer r is called the remainder when n is divided by q. What is remainder when -100 is divided by 30?
A. -20
B. -10
C. 0
D. 10
E. 20
A. -20
B. -10
C. 0
D. 10
E. 20
12 Apr 2024, 00:42
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mattsu
First of all, note that a remainder is always a non-negative integer.
The process for finding the remainder when dividing a negative integer by a positive integer follows the same principles as when dividing a positive integer by a positive integer.
For example:
- What is the remainder when dividing 21 by 6? We find the closest multiple of 6 that is less than 21, which is 18. Then, we calculate (dividend) - (closest multiple less than the dividend) = 21 - 18, yielding a remainder of 3.
- What is the remainder when dividing -23 by 7? Here, we find the closest multiple of 7 that is less than -23, which is -28. Then, we calculate (dividend) - (closest multiple less than the dividend) = -23 - (-28), resulting in a remainder of 5.
What about dividing -100 by 30? The closest multiple of 30 less than -100 is -120. So, the remainder is (dividend) - (closest multiple less than the dividend) = -100 - (-120) = 20.
Alternatively, consider this method:
- What is the remainder when dividing -23 by 7? Dividing 23 by 7 gives a remainder of 2. To find the remainder for -23 divided by 7, subtract this 2 from the divisor. Thus, the remainder when dividing -23 by 7 is 7 - 2 = 5.
Similarly, what is the remainder when dividing -100 by 30? Dividing 100 by 30 gives a remainder of 10. Therefore, the remainder when dividing -100 by 30 is 30 - 10 = 20.
Answer: E
Hope it helps.
08 Apr 2024, 05:00
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nick13
When x is divided by 5, the remainder is 3.
In other words, x is 3 more than a multiple of 5:
x = 5m + 3
When -100 is divided by 30, the remainder is r.
In other words, -100 is r more than a multiple of 30:
-100 = 30m + r
We can PLUG IN THE ANSWERS, which represent the value of r.
Since the prompt indicates that r ≥ 0, eliminate A and B.
When the correct answer is plugged in, the value of m must be a negative integer, as required by the prompt.
C: r=0
-100 = 30m + 0
-100 = 30m
m = -100/3
Since m is not an integer, eliminate C.
D: r=10
-100 = 30m + 10
-110 = 30m
m = -110/3
Since m is not an integer, eliminate D.
E: r=20
-100 = 30m + 20
-120 = 30m
m=-4
Success!
