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

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The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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04 Apr 2018, 16:15
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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

Kudos for the right solution and explanation

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Re: The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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04 Apr 2018, 18:11
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Since the remainder when m + n is divided by 12 is 8, the lowest value of m + n is 8. So we can write m+n=8. By the same logic, we can write m-n=6. Solving the 2 equations yields m=7, n=1. The remainder of 7*1/6 is 1.

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The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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04 Apr 2018, 19:31
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carcass wrote:
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

Kudos for the right solution and explanation

Easiest and best way would be as also shown above:-
take the least possible values of m and n
so $$m+n=8$$ And $$m-n=2$$..
Add two equations.. $$m+n+m-n=8+6....2m=14...m=7$$
So n = 1..
$$mn=7*1=7$$...
Thus remainder will be 1 when 7 is divided by 6..

Now a proper understanding..
If m+n leaves a remainder of 8 when divided by 12, it will leave a remainder of 8-6=2 when divided by 6..
Similarly m-n leaves a remainder of 6 when divided by 12, it will leave a remainder of 6-6=0 when divided by 6..

So m and n leave the same remainder when divided by 6..
But m+n leaves a remainder of 2, so only possiblity is when both m and n leave a remainder of 1 each..

So mn will leave a remainder of 1*1=1
A
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Re: The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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04 Apr 2018, 22:49
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carcass wrote:
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

Kudos for the right solution and explanation

m+n=12k+8
m-n=12l+6

using these eq
m=6(some contant)+7
n=6(some contant)+1
m*n=(6(a)+1)*(6(b)+7)

by remainder theorem remainder is 1

option A
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The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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05 Apr 2018, 16:08
Provided by the question:

1) (m+1)/ 12 = q+8
2) (m-n)/ 12 = q+6
3) m>n

rearranging the equations:
1) m+n = 12q + 8
2) m-n = 12q + 6

Subtracting equation 1 from equation 2, you get 2n = 2 or n=1.

Plugging n=1 back in both equations, you get

m = 12q+ 7.

Now, if q=0, then m=7.

Now you have both values for n and m.
n*m = 1*7 = 7.

7/6 will have a remainder of 1.

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Posts: 1192
Re: The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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06 Apr 2018, 11:21
carcass wrote:
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

another approach:
let difference between quotients=1
equation 1: m+n-8=12q
equation 2: m-n-6=12(q-1)=12q-12
subtracting equation 2 from 1,
2n-2=12
n=7
if q-1=0, then q=1
m+7-8=12*1
m=13
13*7=91
91/6 gives a remainder of 1
A
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Re: The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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06 Apr 2018, 11:33
1
(m+1)/ 12 = q+8
(m-n)/ 12 = q+6
m>n

m+n = 12q + 8
m-n = 12q + 6

2n = 2 or n=1.

m = 12q+ 7.

n*m = 1*7 = 7.

7/6 will have a remainder of 1.
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Re: The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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06 Apr 2018, 11:49
(m+1)/ 12 = q+8
(m-n)/ 12 = q+6
m>n

m+n = 12q + 8
m-n = 12q + 6

2n = 2 or n=1.

m = 12q+ 7.

n*m = 1*7 = 7.

7/6 will have a remainder of 1.
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Re: The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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08 Apr 2018, 06:48
1
Since the remainder when m + n is divided by 12 is 8, the lowest value of m + n is 8. So we can write m+n=8. By the same logic, we can write m-n=6. Solving the 2 equations yields m=7, n=1. The remainder of 7*1/6 is 1.
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The remainder when m + n is divided by 12 is 8, and the remainder when  [#permalink]

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29 Apr 2019, 03:56
m + n = 12a + 8
m - n = 12b + 6

2m = 12 (a + b) + 14
m = 6 (a + b + 1) + 1 (From this we can say m is a number, which when divided by 6 leaves a remainder of 1)

Subtracting both,

2n = 12 (a - b) + 2
n = 6 (a - b) + 1 (From this we can say n is a number, which when divided by 6 leaves a remainder of 1)

When m and n are multiplied and divided by 6, we get a remainder of 1 for each number. Hence the remainder when mn is divided by 6 is 1.

OPTION: A
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The remainder when m + n is divided by 12 is 8, and the remainder when   [#permalink] 29 Apr 2019, 03:56
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