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The remainder when m + n is divided by 12 is 8, and the remainder when
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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
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04 Apr 2018, 18:11
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 mn=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
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04 Apr 2018, 19:31
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 \(mn=2\).. Add two equations.. \(m+n+mn=8+6....2m=14...m=7\) 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 86=2 when divided by 6.. Similarly mn leaves a remainder of 6 when divided by 12, it will leave a remainder of 66=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
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04 Apr 2018, 22:49
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 mn=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
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05 Apr 2018, 16:08
Provided by the question:
1) (m+1)/ 12 = q+8 2) (mn)/ 12 = q+6 3) m>n
rearranging the equations: 1) m+n = 12q + 8 2) mn = 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
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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+n8=12q equation 2: mn6=12(q1)=12q12 subtracting equation 2 from 1, 2n2=12 n=7 if q1=0, then q=1 m+78=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
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06 Apr 2018, 11:33
(m+1)/ 12 = q+8 (mn)/ 12 = q+6 m>n
m+n = 12q + 8 mn = 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
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06 Apr 2018, 11:49
(m+1)/ 12 = q+8 (mn)/ 12 = q+6 m>n m+n = 12q + 8 mn = 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
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08 Apr 2018, 06:48
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 mn=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
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29 Apr 2019, 03:56
m + n = 12a + 8 m  n = 12b + 6 Adding both, 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
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