Latest TCS Aptitude Question SOLUTION: If m+n is divided by 12 then the remainder is 8. And if m-n is divided by 12 then the remainder is 6. Find out the remainder when mn is divided by 6.

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If m+n is divided by 12 then the remainder is 8. And if m-n is divided by 12 then the remainder is 6. Find out the remainder when mn is divided by 6.

Asked In TCS TCS 2014 (11 years ago)

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Neelam Khilwani  (11 years ago)

m+n when divide by 12 leaves rem 8=> 12x+8=m+n
m-n when divided by 12 leaves rem 6=> 12y+6=m-n
Solving both we get m=6(x-y)+1 and n=6(x+y)+7
mn will give u (6(6(x+y)(x-y))+7)/6 .So 36*(any thing ) would leav 0 rem,7 when divide would leav 1 as rem

Is this solution Helpfull? Yes (29) | No (1)  

Mahesh Reddy  (8 years ago)

Let M+N=20 (Bcoz So As To Leave Remainder as 8 When Divided By 12)

Let M-N=18 (So As To Leave The Remainder As 6 When Divided By 12)

By Solving Above 2 Equations We Get M=19 & N=1

Then M*N= 19 When Divided by 6 Gives Remainder as 1

So Ans Is Remainder Equal To 1

Is this solution Helpfull? Yes (19) | No (1)  

Arpit Varshney  (11 years ago)

REMAINDER IS 1....@SRAVYA PLZZ RECHECK UR ANSWER...ND 25*7=175 NOT 105 MIND IT...:)

Is this solution Helpfull? Yes (10) | No (2)  

Abhishek Tiwary  (9 years ago)

let us assume m+n=20
and m-n=18
now,find m and n
then m×n
check it by dividing 6
and then the solution.

the answer will be 1.
By assuming things you can get rid of long equations :)

Is this solution Helpfull? Yes (8) | No (1)  

Sravya Reddy V  (11 years ago)

from the given data m=25,n=7
m+n=32,32/12=8(remainder)
m-n=18,18/12=6(remainder)
m*n=105,105/6=3(remainder)
hence 3 is the ans..

Is this solution Helpfull? Yes (4) | No (10)  

Richik Boral  (9 years ago)

m+n=12x+8
m-n=12y+6
(m+n)/12= 0 rem + (8/12)
then (m+n)=8
so num. can be replaced by its remainder
similarly
(m-n)=6 solving equ , m=7 & n=1
therefore 7/6 rem is 1.

Is this solution Helpfull? Yes (4) | No   

Sravya Reddy V  (11 years ago)

ya sorry 25*7=175
so remainder for 175/6=1

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

Lakshmi  (11 years ago)

sry rem is not 7
1 is correct answer

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

Devika.R  (11 years ago)

hi Sravya,how we will find 25 and 7 value during the short time of exam

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

prince kumar  (9 years ago)

m + n = 12a + 8 ⇒ (m+n)2=144a2+192a+64 - - - (1)(squaring both sides)
m - n = 12b + 6 ⇒ (m−n)2=144b2+144b+36 - - - (2)
(1) - (2) ⇒ 4mn = 144a2+192a−144b2−144b+28
mn = 36a2+48a−36b2−36b+7
Now mn is divided by 6, all the terms except 7 gives 0. So 7 divided by 6, remainder = 1

Is this solution Helpfull? Yes (1) | No   

Lakshmi  (11 years ago)

remainder is 7

Is this solution Helpfull? Yes | No (6)  

s.sahithi  (11 years ago)

1 wil be the remaindrr

Is this solution Helpfull? Yes | No   

Guru Pranav  (11 years ago)

would leav 1 as rem

Is this solution Helpfull? Yes | No   

Khademul Islam  (9 years ago)

let m+n=32------eqn(1)
m-n=30-------eqn(2)
solving both eqn 1 & 2 we get
m=31 and n=1 then mn=31
and from Q mn/6
(31*1)/6=1
hence Remainder will be 1 ans

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routh mahesh  (8 years ago)

m+n-8 when divide by 12 gives remainder 0 => m+n-8/12=0 =>m+n-8=0
m-n-6 when divide by 12 gives remainder 0 =>m-n-6/12=0 => m-n-6=0
solving m+n-8=0 and m-n-6=0 we will get m=7,n=1
mn/6 =>7/6 gives remainder 1

Is this solution Helpfull? Yes | No (1)  

vignesh  (8 years ago)

m + n = 12a + 8 ⇒ (m+n)2=144a2+192a+64
(m+n)2=144a2+192a+64
- - - (1)
m - n = 12b + 6 ⇒ (m−n)2=144b2+144b+36
(m−n)2=144b2+144b+36
- - - (2)
(1) - (2) ⇒ 4mn = 144a2+192a−144b2−144b+28
144a2+192a−144b2−144b+28

mn = 36a2+48a−36b2−36b+7
36a2+48a−36b2−36b+7

Now mn is divided by 6, all the terms except 7 gives 0. So 7 divided by 6, remainder = 1

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vichithra vijayakumar  (6 years ago)

wwould leave 1 as remainder

Is this solution Helpfull? Yes | No   

Akshay Gaikwad  (6 years ago)

Let to get remainder 8
M+N=20
Also to get remainder 6
M-N=18
By solving the equation we get m=19
N=1
So using m and n value we get remainder 1 if the M*Nnumber is divided by 6

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