Latest TCS Aptitude Question SOLUTION: when m+n is divided by 12 the reminder is 8 and m-n is divided by 12 the reminder is 6.what is the reminder when mn is divided by 6??

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when m+n is divided by 12 the reminder is 8 and m-n is divided by 12 the reminder is 6.what is the reminder when mn is divided by 6??

Asked In TCS Afreen shaik (11 years ago)

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shubham  (11 years ago)

according to the given condition
m+n = 12x+8
m-n = 12y+6
on solving we get m = 6x+6y+7, n = 6x-6y+1
so mn = (6x+6y+7)(6x-6y+1) = 36(x^2-y^2)+6x+6y+42x-42y+7
this expression is equal to 6z+1 so on dividing it by 6 we will get 1 as reminder

Is this solution Helpfull? Yes (34) | No (4)  

raj  (11 years ago)

Remainder is always 1
This answer can be proved with multiple values... 2 of them are :-
1. m=7 n=1
2. m=19 n=1

For m=7,n=1
m+n = 8 divide by 12 gives remainder 8
m-n = 6 divide by 12 gives remainder 6
so, m*n = 7 divide by 6 gives remainder 1


For m=19,n=1
m+n = 20 divide by 12 gives remainder 8
m-n = 18 divide by 12 gives remainder 6
so, m*n = 19 divide by 6 gives remainder 1

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Ayush Gupta  (11 years ago)

answer is 1
here m is 19 and n is 1.
m+n = 20 leaves 8 when divided by 12.
m-n = 18 leaves 6 when divided by 12.
mn = 19 leaves 1 when divided by 6.

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vignesh raghupathi  (11 years ago)

7 and 1

(7+1)%12=8
(7-1)%12=6

Is this solution Helpfull? Yes | No (1)  

sanchit shukla  (11 years ago)

this can be done with assuming two no.
49+7=56 give remainder 8
49-7=42 give remainder 6
49*7/6 remainder =1

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sourav  (10 years ago)

Since the remainder when m+n is divided by 12 is 8, m+n=12p+8;
and since the remainder when m–n is divided by 12 is 6, m–n=12q+6.

Here, p and q are integers. Adding the two equations yields 2m=12p+12q+14.
Solving for m yields m=6p+6q+7=6(p+q+1)+1=6r+1,
where r is a positive integer equalling p+q+1.

Now, let’s subtract the equations m+n=12p+8 and m–n=12q+6.
This yields 2n=(12p+8)–(12q+6)=12(p–q)+2.

Solving for n yields n=6(p–q)+1=6t+1,
where t is an integer equalling p–q

Hence, we have mn=(6r+1)(6t+1)=36rt+6r+6t+1=6(6rt+r+t)+1 by factoring out 6

Hence, the remainder is 1

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