Latest TCS Aptitude Question SOLUTION: If m+n gives remainder 8 and m-n gives remainder 6 when divided by 12, then what is the remainder when mn is divided by 6?

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If m+n gives remainder 8 and m-n gives remainder 6 when divided by 12, then what is the remainder when mn is divided by 6?

Asked In TCS Kritika (9 years ago)

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Divya  (9 years ago)

Answer is 1
m+n=12x+8-------let x be divisor in this case
m-n=12y+6-------let y be divisor in this case
from the above two equations
2m=12(x+y)+14
2n=12(x-y)+2
now multiplying the above two we get
mn=12*3(x2-y2)+6(x+y)+42(x-y)+7
On dividing the above equation with 6 we get "1" as remainder

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Ramana Jajula  (9 years ago)

Assume that a is the remainder when m is divided by 12 and b is the remainder when n is divided by 12

then a + b = 8 and a-b = 6

or a = (8+6)/2 = 7 and b = 1

When mn is divided by 6, the remainder will be the remainder of (7*1)/6 which is 1

Is this solution Helpfull? Yes (4) | No   

Pradeep Kumar Gautam  (9 years ago)

(m+n)/12 = 8
=> m+n = 96...........(i)
& (m-n)/12 = 6
=> m-n = 72............(ii)
from (i) and (ii) we get,
m= 168 and n= 12
now, (m*n)/6= 168*12/6
= 168 ans.

Is this solution Helpfull? Yes (1) | No (4)  

rajesh kumar  (9 years ago)

Dividend=divisor×quot+rem
M+n=12×q+8
M-n=12q+6
0n solving these we have m=84&n=12
So ans comes 168

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