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

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VP
Joined: 03 Apr 2007
Posts: 1339

Kudos [?]: 859 [0], given: 10

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

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06 Jul 2008, 21:25
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15% (low)

Question Stats:

73% (00:59) correct 27% (00:43) wrong based on 106 sessions

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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

Kudos [?]: 859 [0], given: 10

Director
Joined: 14 Aug 2007
Posts: 726

Kudos [?]: 220 [0], given: 0

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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)

Kudos [?]: 220 [0], given: 0

Current Student
Joined: 06 Sep 2013
Posts: 1972

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

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

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06 Oct 2013, 09:11
1
KUDOS
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

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

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [1], given: 12324

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

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06 Oct 2013, 09:15
1
KUDOS
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

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;

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-the-integer-k-is-divided-by-12-the-remainder-is-3-whi-102357.html
_________________

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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