Manhattan GRE 2nd edition check your skills question 28

[diksha.mongia]

x has remainder as 4 when divided by 9 and y has remainder 3 when divided by 9 what is the remainder when xy is divided by 9.

can someone explain the answer for this

[tommywallach]

The explanation in the book is probably better than what I'll do here, but I'll do my best!

If a number has a remainder of 4 when it's divided by 9, that means it's 4 greater than some multiple of 9. So possible options are:

4, 13, 22, 31, 40, etc.

That's ALL you know about it, so you can't pin it to an individual number yet.

If y has a remainder of 3 when divided by 9, it's 3 greater than a multiple of 9, so options are:

3, 12, 21, 30, 39, etc.

So if we want to check remainders, we can use any of these:

3*4 = 12 - Has a remainder of 3 when divided by 9
13 * 3 = 39 - Has a remainder of 3 when divided by 9
13 * 12 = 156 - has a remainder of 3 when divided by 9

But you would only need to test one of these of course, because it will always be the same by definition.

-t

[compravu007]

x has remainder as 4 when divided by 9 and y has remainder 3 when divided by 9 what is the remainder when xy is divided by 9.

can someone explain the answer for this

x=9*n+4 :n=1,2,3......

y=9*n+3 :n=1,2,3.....

therefore, x can be (9*1+4=13), (9*2+4=22 and so on....just replace n=1,2,3)&
similarly y can be (9*1+3=12, 9*2+3=21 and so on)

take any two values; x and y, say, x=12 and y=12

divide x*y by 9, u will get remainder 3 OR take any combination of x and y values, u will always get the same result


ONE ALTERNATIVE WAY:: if u find similar question, then simply multiply the remainder(in this case 4*3) and divide by 9 to get remainder.
this way u can save ur time as well

[tommywallach]

Mostly just a repeat of what I said, but I like the alternative method!