Remainder

Question

Hi guys, I have this question:

If x has a remainder of 4 when divided by 9 and y has a reminder of 3 when divided by 9, what's the remainder when xy is divided by 9?

Thanks in advance for the attention received!!!!

mikemcgarry · Answer

Dear arturo2021 , I'm happy to respond :-)

, but I'm a little confused because you appear to have posted the solution to the question about which you are asking. Are you suggesting that this particular explanation does not make sense to you? First of all, here's a blog on remainders. https://magoosh.com/gmat/2012/gmat-quant ... emainders/ My explanation will not be all that different from what is said in that explanation you posted, but perhaps a different way of saying it will resonate. The first statement (" x has a remainder of 4 when divided by 9 ") implies: x = (some THING divisible by 9) + 3 = A + 3 and the second implies y = (some OTHER THING divisible by 9) + 4 = B + 4 I abbreviated those long phrases with A & B for algebraic clarity. Now we multiply --- for the two expressions with addition, we have to FOIL. See this blog on FOILing: https://magoosh.com/gmat/2012/foil-on-th ... expanding/ x*y = (A + 3)*(B + 4) = A*B + 4A + 3B + 12 Since A & B are both divisible by 9, any term with either an A or a B in it will be divisible by 9 --- that's the first three terms. Since those first three terms are divisible by 9, by definition they have a remainder of zero. The only term that could possibly leave a remainder is the last term. 12 divided by 9 has a remainder of 3. Does all this make sense? Mike :-)

rrsnathan · Answer

Hi Arturo2021,

Another Method of solving:

For this type of question u can take example values

as x=12 (13/9 = 1 (quotient) + 4 (Remainder)) and y =12 (12/9 = 1 (quotient) + 3 (Remainder))

So xy = 156
xy/9 = 17 (Quotient) + 3(Remainder)
So answer is 3.

Thanks,
Rrsnathan.

Presssssss kudos if helped

mau5 · Answer

Once you read such questions, it would be better to understand that the remainder when xy is divided by 9, would be the SAME, for any values of x and y, given the fact that they individually adhere to the conditions given. Thus, just pick up numbers for x and y.

For x=4, the remainder when 4 is divided by 9=4(Condition 1 met,Check)
For y=3, the remainder when 3 is divided by 9=3(Condition 2 met,Check)

Thus, xy=12, and when 12 is divided by 9, the remainder is 3.
You can plug in ANY relevant values for (x,y) and will still get the remainder as 3.

Hope this helps.

Remainder

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