Latest TCS Aptitude Question SOLUTION: If m+n gives remainder as 8 and m-n gives remainder as 6 when both are divide by 12, what is the remainder when m*n is divided by 6?

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If m+n gives remainder as 8 and m-n gives remainder as 6 when both are divide by 12, what is the remainder when m*n is divided by 6?

Asked In TCS PRIYA NAMDEO (10 years ago)

Solved sravan Read Solution (12)

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Read Solution (12) :

sravan  (10 years ago)

let
m+n=12a+8
m-n=12b+6
m*n=(6*(a+b)+7)(6*(a-b)+1))
7%6=2
ans = 1

Is this solution Helpfull? Yes (31) | No (1)  

Kushal Saraf  (10 years ago)

Let m=13,n=7
hence
m+n=20 and 20%12=8
m-n=6 and 6%12= 6
m*n= 91 and 91/6=1

Is this solution Helpfull? Yes (14) | No   

Pratibha Agrawal  (10 years ago)

let no m = 7 n=1
then both given condition satisfy this
so 7/6 gives 1 as a remainder
so , 1

Is this solution Helpfull? Yes (4) | No   

Mahesh  (10 years ago)

As there is confusion regarding the answer, i am giving an example of values for M and N

Let M=19 and N= 13;
Remainder when (M+N), that is (19+13) divided by 12 = 8
Remainder when (M-N), that is (19-13) divided by 12 = 6
Remainder when (M*N), that is (19*13)= 247 divided by 12 = 7

So, 7 is the answer

Is this solution Helpfull? Yes (3) | No (6)  

Mahesh  (10 years ago)

Lets assume the remainders when these numbers are divided by 12 be a and b respectively.

The remainder when these two numbers are added, that is M+N is divided by 12 is nothing but the sum of a and b, so a+b is 8
The remainder when M-N is divided by 12 will be either (a-b) 0r 12-(b-a), in the case, b>a
If, a+b = 8 and a-b =6: a=7 and b=1
If a+b=8, 12-(b-a)=6: here a=1 and b=7

Example for the first case is numbers 31 and 13
Example for the second case is 109 and 67

But the question is not asking about the values of a and b, but only the product of a and b, that is the remainder when the product of M and N is divided by 12, that will be 7*1=7
Answer is 7

Is this solution Helpfull? Yes (2) | No (16)  

Manohar  (10 years ago)

answer 1..............

Is this solution Helpfull? Yes (2) | No   

Arun Menariya  (10 years ago)

m+n=12k+8;
m-n=12p+6;
4*m*n=(m+n)^2-(m-n)^2
ans is 7

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

sandeep gantait  (10 years ago)

m+n/12=8;m+n=96
m-n/12=6;m-n=72
m=82;n=12
m*n/6=82*12/6=164

Is this solution Helpfull? Yes | No (8)  

Mahesh  (10 years ago)

As it is 6 in the question, 1 is the answer.
Sorry for the confusion

Is this solution Helpfull? Yes | No   

hitesh kumar gupta  (10 years ago)

answer is 7

Is this solution Helpfull? Yes | No (2)  

naveen  (10 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 4
i.e (14*2)/6

Is this solution Helpfull? Yes | No   

satyam  (9 years ago)

M=19
N=1
M*N=19%6=1

Is this solution Helpfull? Yes | No   

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