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When the integer k is divided by 12, the remainder is 3.

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When the integer k is divided by 12, the remainder is 3. [#permalink] New post 06 Jul 2008, 20:25
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68% (02:01) correct 33% (00:47) wrong based on 39 sessions
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-the-integer-k-is-divided-by-12-the-remainder-is-3-whi-102357.html
[Reveal] Spoiler: OA
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Re: PS-remainder [#permalink] New post 06 Jul 2008, 20:34
goalsnr wrote:
14. 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


is it E.

k = 12*a + 3

2k = 12*2*a + 6
6k = 12*6*a + 18 ( 18 = 12+6)
4k + 6 = 12*4*a + 18 (18 = 12 + 6)
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Re: When the integer k is divided by 12, the remainder is 3. [#permalink] New post 06 Oct 2013, 08:11
goalsnr wrote:
14. 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


OA please. IMO it is E.
We just need to express k=12q+3 and then perform all the operations and take remainders given.
I,II and III all true

I like Kudos 8-)
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Re: When the integer k is divided by 12, the remainder is 3. [#permalink] New post 06 Oct 2013, 08:15
Expert's post
jlgdr wrote:
goalsnr wrote:
14. 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


OA please. IMO it is E.
We just need to express k=12q+3 and then perform all the operations and take remainders given.
I,II and III all true

I like Kudos 8-)


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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-the-integer-k-is-divided-by-12-the-remainder-is-3-whi-102357.html
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Re: When the integer k is divided by 12, the remainder is 3.   [#permalink] 06 Oct 2013, 08:15
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When the integer k is divided by 12, the remainder is 3.

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