A positive number when divided by 88 gives the remainder 8. What will be the remainder when this number id divided by 11 ?

Question

anonymous · Answer

3?

anonymous · Answer

lets try it.  what number when divided by 88 gives a remainder of 8? well 88+8=96 for for one

vishweshshrimali5 · Answer

Yes I have done hit and trial and what i have got is that the remainder = 8

anonymous · Answer

so i guess 3 is wrong because 
$$\frac{96}{11}=8\tfrac{8}{11}$$ so remainder is 8.  shows you what i know!

vishweshshrimali5 · Answer

But how will you prove it

vishweshshrimali5 · Answer

I want the whole  explanation for it

anonymous · Answer

and we can try it again with 
$$2\times 88 + 8$$

anonymous · Answer

oh now that we know it is 8, i think answer is easy enough

vishweshshrimali5 · Answer

Yes that also gives remainder 8

vishweshshrimali5 · Answer

But how will you prove it

anonymous · Answer

because 
$$88=8\times 11$$ yes?

vishweshshrimali5 · Answer

Right !

vishweshshrimali5 · Answer

Now what to do ?

anonymous · Answer

so 
$$n\times 88+8=11n+8$$

vishweshshrimali5 · Answer

Now !

anonymous · Answer

and when you divide 
$$11n+8$$ by 11 you get a remainder of 8

vishweshshrimali5 · Answer

How ?

anonymous · Answer

since clearly11 divides 11n  evenly!

vishweshshrimali5 · Answer

Yes

vishweshshrimali5 · Answer

And we get 8 as remainder

vishweshshrimali5 · Answer

Thanks

anonymous · Answer

that is all you need.  11 goes in to "11n" n times, so it goes in to 11n + 8 n times with a remainder of 8.yw

vishweshshrimali5 · Answer

Thanks

vishweshshrimali5 · Answer

But how did you get n×88+8=11n+8

vishweshshrimali5 · Answer

I can't get that still ?

vishweshshrimali5 · Answer

Because if I will show that using hit and trial I got this
My teacher will give me zero marks

vishweshshrimali5 · Answer

Please help !!!!

anonymous · Answer

what to you mean "hit and trial"? we proved it

vishweshshrimali5 · Answer

How did we prove that n×88+8=11n+8

anonymous · Answer

just say "if n is divided by 88 and the remainder is 8, then 
$$n=88k+8$$ and therefore 
$$n=11\times 8j+8$$ since 
$$88=11\times 8$$

vishweshshrimali5 · Answer

Ok
Then ?

anonymous · Answer

'thus upon dividing 
$$n=11\times 8j+8$$ by 11 we see that 11 divides 
$$11\times 8j$$ evenly giving a remainder of 8"
qed 
aka 
have a nice day

vishweshshrimali5 · Answer

Thanks a lot satellite

vishweshshrimali5 · Answer

Will you please help me in some more questions

vishweshshrimali5 · Answer

Go to my profile page and then to the questions asked

anonymous · Answer

post them be happy to

vishweshshrimali5 · Answer

Ok