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11 Sep 2010, 01:53
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (01:50) correct
25%
(02:02)
wrong
based on 1372
sessions
History
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Not Attempted Yet
When the integer k is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6?
I. 2k
II. 6k
III. 4k+6
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I,II, and III
I. 2k
II. 6k
III. 4k+6
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I,II, and III
06 Oct 2010, 12:44
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niheil
Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).
So we are given: \(k=12q+3\).
I. 2k --> \(2k=2(12q+3)\) --> \(2k=2*12q+6=12*(2q)+6\) --> \(2k\) divided by 12 yields reminder of 6;
II. 6k --> \(6k=6(12q+3)\) --> \(6k=6*12q+18=12*(6q)+12+6=12(6q+1)+6\) --> \(6k\) divided by 12 yields reminder of 6;
III. 4k + 6 --> \(4k+6=4(12q+3)+6\) --> \(4k+6=12*(4q+1)+6\) --> \(4k+6\) divided by 12 yields reminder of 6;
Answer: E.
General Discussion
11 Sep 2010, 02:05
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Capthan
\(k=12m+3\) where m is an integer
\(2k=24m+6\) so remainder with 12 is 6
\(6k=72m+18=12(6m+1)+6\) so remainder with 12 is 6
\(4k+6=48m+18=12(4m+1)+6\) so remainder with 12 is 6
So (E) is the answer
