Remainders QR #165 PS

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by anshumishra » Sun Jan 16, 2011 4:38 pm
tonebeeze wrote:When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

a. 3
b. 4
c. 7
d. 8
e. 12

OA: 7
This would be really fast if you use the options :

3 - no chance as n-4 would be 3-4 = -1
4 - R(10/4) = 2 ≠ 4-4
7 - R(10/7) = 3 = 7-4 --- Answer, stop here
8 - R(10/8) = 2 ≠ 8-4
12 - R(10/12) = 10 ≠ 12 - 4

Hence : C
Thanks
Anshu

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by Rahul@gurome » Sun Jan 16, 2011 6:50 pm
A different approach:
When 10 is divided by the positive integer n, the remainder is n-4.
This means 10 = n*k + (n-4), where k is an integer.
Or 10 = n*(k+1) - 4.
Or 14 = n*(k+1).
Or n divides 14.
Only c. which is 7 satisfies this condition.
The correct answer is c.
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