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When m is divided by 6, the remainder is 3 and when n is divided by 12
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MBA20
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When m is divided by 6, the remainder is 3 and when n is divided by 12 [#permalink] New post  29 Apr 2019, 01:48
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When m is divided by 6, the remainder is 3 and when n is divided by 12, the remainder is 9, where m and n are positive integers. Which of the following could be the value of m+n?

I. 72
II. 108
III. 180

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
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Bunuel
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Re: When m is divided by 6, the remainder is 3 and when n is divided by 12 [#permalink] New post  29 Apr 2019, 01:51
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MBA20 wrote:
When m is divided by 6, the remainder is 3 and when n is divided by 12, the remainder is 9, where m and n are positive integers. Which of the following could be the value of m+n?

I. 72
II. 108
III. 180

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III


You sited the source as Official Guide. Which OG is that question from?
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When m is divided by 6, the remainder is 3 and when n is divided by 12 [#permalink] New post  29 Apr 2019, 01:54
Bunuel wrote:
MBA20 wrote:
When m is divided by 6, the remainder is 3 and when n is divided by 12, the remainder is 9, where m and n are positive integers. Which of the following could be the value of m+n?

I. 72
II. 108
III. 180

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III


You sited the source as Official Guide. Which OG is that question from?


I have re-tagged it to 800 score.
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Re: When m is divided by 6, the remainder is 3 and when n is divided by 12 [#permalink] New post  29 Apr 2019, 02:22
m is of the form 6k+3 or 3,9,15
N is of the form 12l+9 or 9,21,45

M+n should be definitely of form 9l
We see above all three options are multiple of 9 thus all three are possible values of m+n . Hence e

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Re: When m is divided by 6, the remainder is 3 and when n is divided by 12 [#permalink] New post  29 Apr 2019, 02:45
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m = 6a + 3
n = 12b + 9

m + n = 6a + 12b + 12
= 6(a + 2b + 2)

From the above eq, we can say that m + n should definitely be a 6 multiple.

From the options given, all are 6 multiples (72, 108, 180).

OPTION: E
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Re: When m is divided by 6, the remainder is 3 and when n is divided by 12 [#permalink] New post  04 Sep 2019, 12:36
MBA20 wrote:
When m is divided by 6, the remainder is 3 and when n is divided by 12, the remainder is 9, where m and n are positive integers. Which of the following could be the value of m+n?

I. 72
II. 108
III. 180

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III


m is of the form 6k+3 so 3,9,18,27,36,45,54.
n is of the form 12j+9 so 9,21,42,63,84,105,126.
I. 72 - 63+9
II. 108 - 63+45
III. 180 - 126+54

Hence E
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Re: When m is divided by 6, the remainder is 3 and when n is divided by 12 [#permalink] New post  16 Mar 2021, 01:47
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