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Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]
1
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
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Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]
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wouldn't adding m+n to m-n result in m = 12a + 12b + 14, IShanGRE? (the quote function isnt working on my browser atm)
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Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]
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Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]
2
Just choose numbers for m & n.

Choosing m = 7 & n = 1 fullfil all the provided conditions.

Ans: A) 1 when, mn = 7 is divided by 6.
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Re: The remainder when m + n is divided by 12 is 8, and the rema [#permalink]
1
I chose m-n = 18 ( 18%12=6) ; m+n = 20 (20%12=8).

thus the equations :
m - n = 18....(1)
m+ n = 12...(2)
---------------------------
m=19 and n=1

Hence,
mn/6 = 19/6 Gives remainder as 1.

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

Theory: Dividend = Divisor*Quotient + Remainder

m + n -> Dividend
12 -> Divisor
a -> Quotient (Assume)
8 -> Remainder
=> m + n = 12*a + 8 = 12a + 8 ...(1)

The remainder when m - n is divided by 12 is 6

Let Quotient be b

=> m - n = 12b + 6 ...(2)

Adding (1) and (2) we get

m + n + m - n = 12a + 8 + 12b + 6 = 12*(a+b) + 14
=> 2m = 12*(a+b) + 14
=> m = 6*(a+b) + 7 = 6*(a+b+1) + 1

(1) - (2) we get

m + n -( m - n) = 12a + 8 -( 12b + 6) = 12*(a-b) + 2
=> 2n = 12*(a-b) + 2
=> n = 6*(a-b) + 1

=> m*n = (6*(a+b+1) + 1) * (6*(a-b) + 1)
=> on right hand side all terms will be a multiple of 6 except 1*1

=> m*n = multiple of 6 + 1
=> m*n will give 1 remainder when divided by 6

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Remainders

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