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16 Sep 2014, 01:03
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When a positive integer \(n\) is divided by 4, the remainder is 3. Which of the following could be the remainder when \(n\) is divided by 12?
A. 2
B. 4
C. 6
D. 10
E. 11
A. 2
B. 4
C. 6
D. 10
E. 11
16 Sep 2014, 01:03
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Official Solution:
When a positive integer \(n\) is divided by 4, the remainder is 3. Which of the following could be the remainder when \(n\) is divided by 12?
A. 2
B. 4
C. 6
D. 10
E. 11
A positive integer \(n\), when divided by 4, leaves a remainder of 3, can be expressed as \(n = 4q + 3 = even + odd = odd\).
Thus, \(n\) is odd. An odd integer, when divided by 12, cannot leave an even remainder; so, the only viable option is E (for example, consider \(n=35\)).
Answer: E
When a positive integer \(n\) is divided by 4, the remainder is 3. Which of the following could be the remainder when \(n\) is divided by 12?
A. 2
B. 4
C. 6
D. 10
E. 11
A positive integer \(n\), when divided by 4, leaves a remainder of 3, can be expressed as \(n = 4q + 3 = even + odd = odd\).
Thus, \(n\) is odd. An odd integer, when divided by 12, cannot leave an even remainder; so, the only viable option is E (for example, consider \(n=35\)).
Answer: E
25 Dec 2016, 07:07
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This Question Confuses me ....
n=4q+3.... so basically its 7,11,15,19,23,27.....
when same n is divided by 12, lets consider the series from 15 onwards....the remainders will be 3,7,9 in same repeating fashion every 3 nos...
what is wrong in my thought process ??
n=4q+3.... so basically its 7,11,15,19,23,27.....
when same n is divided by 12, lets consider the series from 15 onwards....the remainders will be 3,7,9 in same repeating fashion every 3 nos...
what is wrong in my thought process ??
