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# The remainder when m + n is divided by 12 is 8, and the rema

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The remainder when m + n is divided by 12 is 8, and the rema [#permalink]  14 Apr 2018, 02:42
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Question Stats:

61% (02:27) correct 38% (01:33) wrong based on 13 sessions
The remainder when m + n is divided by 12 is 8, and the remainder when m - n is divided by 12 is 6. If $$m > n$$, then what is the remainder when mn divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

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Director
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Kudos [?]: 477 [2] , given: 84

Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]  20 Apr 2018, 04:05
2
KUDOS
List few members for $$m + n$$. for eg. $${8, 20, 32}$$
List few members for the set $$m-n$$. for eg. $${6,18,30}$$

now make a equation by chosing any pair of values

$$m+n = 8...........i$$
$$m-n = 6...........ii$$

subtracting eqn $$ii$$ from $$i$$ we get,
$$2n =2 or n =1$$

Putting $$n =1$$ in eqn $$i$$ we get $$m + 1 = 8 or m = 7$$
therefore$$m*n = 7$$
$$\frac{7}{6}$$ gives a remainder of $$1$$
option A
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Intern
Joined: 28 Nov 2017
Posts: 44
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Kudos [?]: 30 [1] , given: 22

Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]  20 Apr 2018, 21:47
1
KUDOS
A. 1

Solution :
m+n = 12a + 8 (i)
m-n = 12b+ 6 (ii)

m = 6(a+b) + 7

put m in any eqn. and you get n = 6(a-b)+1

multiply m*n = 6* Some Integer + 7

So remainder will be decided by 7

7/6 remainder = 1
Manager
Joined: 29 Nov 2017
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GRE 1: Q142 V146
WE: Information Technology (Computer Software)
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Kudos [?]: 77 [1] , given: 99

Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]  24 Apr 2018, 09:46
1
KUDOS
I simply solved it by the following method,

m+n = 12q +8 equation 1

m-n = 12q +6 equation 2

since we know that to a find range of equation 1 and equation 2 we need to apply the following rule

1 ---> 12 * 1 + 8 = 20
12 * 2 + 8 = 32
12 * 3 + 8 = 44
12 * 4 + 8 = 56----etc

2 12 * 1 + 6 = 18
12 * 2 + 6 = 30
12 * 3 + 6 = 42
12 * 4 + 6 = 52

now we can use the first values of the above lists 20 * 18 =360/6 leads to 60 remainder 1 and can check with other values as well -- so the answer is A
Re: The remainder when m + n is divided by 12 is 8, and the rema   [#permalink] 24 Apr 2018, 09:46
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