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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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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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New post 04 Apr 2018, 17:11
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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.

Answer: 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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New post 04 Apr 2018, 18:31
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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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New post 04 Apr 2018, 21:49
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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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New post 05 Apr 2018, 15:08
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.

Answer 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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New post 06 Apr 2018, 10:21
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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New post 06 Apr 2018, 10:33
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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New post 06 Apr 2018, 10:49
(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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New post 08 Apr 2018, 05:48
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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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Re: The remainder when m + n is divided by 12 is 8, and the remainder when &nbs [#permalink] 08 Apr 2018, 05:48
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