remainders

[joannabanana]

If x and y are positive integers, what is the remainder when x is divided by y ?

1) When x is divided by 2y, the remainder is 4.
2) when x+y is divided by y, the remainder is 4.

answ b

This is from the Kaplan 800 book and the only solution they give is by picking numbers. I know there's an algebraic way to get the answ, but it's not completely clear in my head. Can one of the experts clarify it?

I remember reading in one of the Manhattan guides that:

if: a/n gives a remainder of 2 and b/n gives a remainder of 3
then: (a+b)/n gives a remainder of 2+3
and: (a*b)/n gives a remainder of 2*3

Is that correct? If so then this could be a way of deducing that 2 is sufficient. I'm not sure how to be certain about 1 though.

[goyalsau]

If x and y are positive integers, what is the remainder when x is divided by y ?

1) When x is divided by 2y, the remainder is 4.
2) when x+y is divided by y, the remainder is 4.

answ b

This is from the Kaplan 800 book and the only solution they give is by picking numbers. I know there's an algebraic way to get the answ, but it's not completely clear in my head. Can one of the experts clarify it?

I remember reading in one of the Manhattan guides that:

if: a/n gives a remainder of 2 and b/n gives a remainder of 3
then: (a+b)/n gives a remainder of 2+3
and: (a*b)/n gives a remainder of 2*3

Is that correct? If so then this could be a way of deducing that 2 is sufficient. I'm not sure how to be certain about 1 though.

Your Both concepts are Absolutely correct


a/n gives a remainder of 2 and b/n gives a remainder of 3
then: (a+b)/n gives a remainder of 2+3
and: (a*b)/n gives a remainder of 2*3

Rahul Given a Brilliant explanation on the this link
https://www.beatthegmat.com/number-syste ... tml#316451

[Geva@EconomistGMAT]

The concepts are correct, but they do not help you with (1), which will require plugging in to make sure that its insufficient. The reason, as you have probably deduced, is that the concepts are all based on the fact that a, b, and a+b are all divided by the same n - you cannot shift this additive/multiplicative property to division by x or 2x.