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

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

Asked In TCS Sonu verma (11 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

Bailore Pradyumna Acharya  (11 years ago)

12a+8=m+n;12b+6=m-n;therefore mn=[6(a+b+1)+1]*[(6(a-b)+1];so the remainder is 1 when divided by 6

Is this solution Helpfull? Yes (35) | No (3)  

Sruthi karuturi  (11 years ago)

m+n=12x+8
m-n=12y=6
m=12(x+y)+14=6(2x+2y)+14
n=12(x-y)+2=6(2x-2y)+2
mn/6 produces a remainder of 4i.e(14*2)/6

Is this solution Helpfull? Yes (18) | No (30)  

nancy  (11 years ago)

m+n=12x+8
m-n=12y+6

solve for m & n
m=6(x+y)+7
n=6(x-y)+1

mn/6=1

Is this solution Helpfull? Yes (15) | No   

lavishpatodi  (11 years ago)

it is given that when sum of digit is divided by 12 gives 8 as a remainder
and their difference divided by 12 gives 6

therefore we have to suppose such numbers whose sum is 20 and difference is 6 by hit n trial we found (13,7) is such pair
m=13 and n=7

on putting m=13 and n=7 in the given condition we get ~

m*n/6=13*7/6=91/6 yields 1 as a remainder

Is this solution Helpfull? Yes (11) | No   

Perumalsamy  (11 years ago)

The ans is=2
(m+n)*12+8
(12m+12n)+8
Let m=5, n=4
(60+48)+8=116
116%12=8 (it also satisfy (m-n))
so m*n=5*4=20
=20%6=2

Is this solution Helpfull? Yes (1) | No (16)  

kalyani dangeti  (11 years ago)

m+n=12x+8.....(1)
m-n=12y+6.....(2)
2m=12(x+y)+14 since adding 2 eq's
m=6(x+y)+7
2n=12(x-y)+2 since subtracting 2 eq's
n=6(x-y)+1
==>mn=(6(x+y)+7)*(6(x-y)+1)
mn%6=7*1=7
ans=7

Is this solution Helpfull? Yes (1) | No (7)  

abhinav kedia  (11 years ago)

ans is 1
m+n=12a+8
m-n=12b=6
=> m=6(a+b)+7=6k+1
& n=6(a-b)+1
therefore, m*n/6 will give remainder as 1

Is this solution Helpfull? Yes (1) | No (2)  

basanagouda  (11 years ago)

R(m+n+m-n)/.....=8+6=14/2====7
M+N-(M-N)=1
MN=1*7=7

Is this solution Helpfull? Yes | No (2)  

PRAVEEN K H  (11 years ago)

4 is the right answer ..
Let us take m=12 and n=8 which satisfies the above condition ...
So m*n=96
96/6 will gives you the remainder 4 ..
100% solved now ..

Is this solution Helpfull? Yes | No (5)  

Guru Pranav  (11 years ago)

here the remainder will be 7 and when it is divided by 6, the remainder will be 1.

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CHANDAN KUMAR  (10 years ago)

m+n=12a+8
m-n=12b+6
2m=12(a+b)+14
m=6(a+b)+7.......(i)
2n=12(a-b)+2
n=6(a-b)+1........(ii)
mn=[12(a+b)+7][12(a-b)+1]=36(a^2-b^2)+6(a+b)+42(a-b)+7
mn/6=7/6=rem=1(ans)

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milan jena  (9 years ago)

m+n=12x+8
m-n=12y+6 so solving above two equation we get
⇒m=6(x+y)+7 and
⇒n=6(x-y)+7
so mn=[6(x+y)+7][6(x-y)+7]
⇒36x^2-36xy+42x+36xy-36y^2+42x+42y-42y+49
⇒36x^2-36y^2+84x+49
when we divide the above equation wrt 6 then remainder is 1.

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Ramya  (9 years ago)

m+n=8
m-n=6
a=m+n/2=8+6/2=14/2=7
b=m-n/2=8-6/2=2/2=1
therefore, mn = 7-1/6=6/6=1

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Darpan  (8 years ago)

mn/6=((m+n)^2/4-(m-n)^2/4)/6 [expanding mn in terms of m+n and m-n];
replace the value of m+n and m-n with the remainder values [as number divided by 6 will give same remainder as number divided by 12];
mn/6 = (8^2/4-6^2/4)/6
i.e, 7/6;
therefor, remainder of mn/6 i.e, mn%6=1

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