me test

Question

On dividing a certain number by 5,7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the number is divided by 8, 7 and 5, the respective remainders will be..…

[Ans given is 5 , 3 , 2 but i am getting as 5 ,5 ,2]

Answer 1

Let the original number be X. Then by the successive dividing we have followings :
X=5A+2
A=7B+3
B=8C+4.

So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.

Now by dividing X by 8, 7, 5 successively we have followings :
X=8*(5*7C+19)+5
5*7C+19=7*(5C+2) + 5
5C+2=5C+2.

 Respective reminders are  5,5,2