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If the remainder is 7 when positive integer n is divided by
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19 Aug 2020, 11:55
19 Aug 2020, 11:55
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If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
Re: If the remainder is 7 when positive integer n is divided by
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19 Aug 2020, 12:48
19 Aug 2020, 12:48
If the remainder is 7 when n is divided by 18 then we can write
n=18k + 7 where k is any integer we want.
n=6*3*k+6+1 = 6(3*k+1)+1=6* an integer + 1
So when we divide n by 6 the remainder is 1.
If you want to be convinced you can take n=25. We have n=18+7 so the remainder is indeed 7 when divided by 18, and n=6*4 + 1 so the remainder is indeed 1 when divided by 6.
n=18k + 7 where k is any integer we want.
n=6*3*k+6+1 = 6(3*k+1)+1=6* an integer + 1
So when we divide n by 6 the remainder is 1.
If you want to be convinced you can take n=25. We have n=18+7 so the remainder is indeed 7 when divided by 18, and n=6*4 + 1 so the remainder is indeed 1 when divided by 6.
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Re: If the remainder is 7 when positive integer n is divided by
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19 Aug 2020, 13:58
19 Aug 2020, 13:58
Carcass wrote:
If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
With many Integer Properties questions, we can often reach the correct answer by simply testing a value that satisfies the given information.
Given: the remainder is 7 when positive integer n is divided by 18
So, n COULD equal 7.
When we divide 7 by 6, the remainder is 1.
Answer: B
Please keep in mind that this strategy will work for ANY value that satisfies the given information.
If the remainder is 7 when positive integer n is divided by 18, n could also equal 25 or 43 or 61 or ...
For any of these possible values of n, the remainder is always 1 when we divide them by 6.
Cheers,
Brent
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