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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]

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New post 06 Jul 2008, 21:25
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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]

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New post 06 Jul 2008, 21:34
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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]

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New post 06 Oct 2013, 09:11
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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-)

Kudos [?]: 740 [1], given: 355

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Re: When the integer k is divided by 12, the remainder is 3. [#permalink]

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New post 06 Oct 2013, 09:15
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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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Kudos [?]: 132517 [1], given: 12324

Re: When the integer k is divided by 12, the remainder is 3.   [#permalink] 06 Oct 2013, 09:15
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When the integer k is divided by 12, the remainder is 3.

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