Remainder Question

[calebjli]

47*49 divided by 8 has what remainder?
I saw the solution in the advanced GMAT.
However I think it can be solved easily like this

47 = 7 mod 8
49 = 1 mod 8

therefore 7 mod 8 is the product

instead of doing any complicated math.

Thanks for your help.

[RonPurewal]

47*49 divided by 8 has what remainder?
I saw the solution in the advanced GMAT.
However I think it can be solved easily like this

47 = 7 mod 8
49 = 1 mod 8

therefore 7 mod 8 is the product

instead of doing any complicated math.

Thanks for your help.

The problem, of course, is that most people -- including me -- don't know what that means. But, if it works, sure! If something works, then it's just as good as anything else that works.

[RonPurewal]

By the way, it's not horribly awful to realize that this is
(48 - 1)(48 + 1)
= 48^2 - 1.
So it's 1 less than a multiple of 8, making the remainder 7.

You mentioned "complicated math", so I'm going to assume you're referring to something substantially more complicated than this. What's the complicated math?

[calebjli]

sorry i think my point was:
i think there are remainder rules like:

for 47 and 49

47 is 7 remainder for 8
49 is 1 remainder for 8

so simple math would be, to multiply it, so the product is 7 remainder for 8.

e.g. let's say for 523 * 529 divided by 8, what is the remainder?
then you would have
3 mod 8 (remainder of 3)* 1 mod 8 (remainder of 1) so the product should be 3 mod 8, so it has a remainder of 3.

I think different methods work for different people, but I wanted to confirm that this methodology works. I studied this 3-4 years ago and couldn't remember.

Essentially: x (A big number) + y (A big number) divided by a z has what remainder?
so if you split it up, x has remainder u and y has a remainder w, then the sum has a remainder of u+w as long as it's less than z.

similarly x * y divided by z, u*w would be the remainder for the product.

[RonPurewal]

so if you split it up, x has remainder u and y has a remainder w, then the sum has a remainder of u+w as long as it's less than z.

similarly x * y divided by z, u*w would be the remainder for the product.

I think this works even if it's equal to or greater than z. You just have to take out z's until it's not, so that your remainder is actually a legitimate remainder.
For instance, if you multiply two numbers that have remainders 5 and 7, respectively, when you divide by 8, you get a "remainder" of 35. That's not a true remainder, though, because you can still take more 8's out of it. Specifically, you can take four 8's out of that and have 3; the product should leave a remainder of 3 when it is divided by 8.
Same with addition.