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

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Capthan
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When the integer k is divided by 12, the remainder is 3. Which of the [#permalink] New post   11 Sep 2010, 01:53
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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
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E
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Bunuel
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Re: A second Problem Solving question [#permalink] New post   06 Oct 2010, 12:44
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niheil wrote:
Please explain to me how to solve the following Problem Solving question. It was listed in one of the GMAT Paper Tests.

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


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.
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Re: When the integer k is divided by 12, the remainder is 3. Which of the [#permalink] New post   11 Sep 2010, 02:05
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Capthan wrote:
When the integer k is divid 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

Answer with explaination will be highly appreciated.


\(k=12m+3\) 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
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Re: When the integer k is divided by 12, the remainder is 3. Whi [#permalink] New post   09 Nov 2014, 02:43
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Picking is safe in this case

take 15=1*12+3

2*15=30/12=2*12+6, so YES
6*15=90/12=7*12+6, so YES
4*15+6=66/12=5*12+6, so YES

E
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Re: A second Problem Solving question [#permalink] New post   06 Oct 2010, 12:56
Awesome! Thanks again Bunuel!
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When the integer k is divided by 12, the remainder is 3. Whi [#permalink] New post   08 Nov 2014, 17:56
Hi Bunnel,

Can you tell me what am I doing wrong?

For Statement 1
k= 12q +3 ---> 3(4q+1)
2k/12 = 3(4q+1)*2/12 ----> 4q+1/2. Anything divided by two has a remainder of either 0 or 1. Where am I going wrong?
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Re: When the integer k is divided by 12, the remainder is 3. Whi [#permalink] New post   08 Nov 2014, 22:04
annie2014 wrote:
Hi Bunnel,

Can you tell me what am I doing wrong?

For Statement 1
k= 12q +3 ---> 3(4q+1)
2k/12 = 3(4q+1)*2/12 ----> 4q+1/2. Anything divided by two has a remainder of either 0 or 1. Where am I going wrong?



It seems you got the PEMDAS wrong

1. Solve the terms inside the brackets.
2. Multiplication
3. Division.
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Re: When the integer k is divided by 12, the remainder is 3. Whi [#permalink] New post   17 Mar 2016, 11:22
Temurkhon wrote:
Picking is safe in this case

take 15=1*12+3

2*15=30/12=2*12+6, so YES
6*15=90/12=7*12+6, so YES
4*15+6=66/12=5*12+6, so YES

E


I did the same and got the correct answer. Just wanted to confirm if this method will be applicable in every such problem!! Please suggest.
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Re: When the integer k is divided by 12, the remainder is 3. Whi [#permalink] New post   16 Apr 2023, 12:50
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Re: When the integer k is divided by 12, the remainder is 3. Whi [#permalink]
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