so I have determined one pattern when we divide a negative integer -x with a positive integer y where x<y, the reminder is the addition of (-x) + y. For example, when we divide -4 by 12 we get 8 as a reminder, and apparently (-4) + 12 = 8. here’s another example when we divide -4 by 11, the remainder is 7 which is apparently the addition of -4 and 7. So is this true when we divide a negative integer -x with a positive integer y where x<y, the remainder is the addition of (-x) + y? To more specified version of my point is here!

So you would have x = -1 \times y + r where x is the negative number and y the divisor and r the remainder.

An example would be

-4 = -1 \times 12 + 8

or yes, the remainder is x + y, where x is the negative number (which you represented as -x).

The key thing to note is that remainders are always non-negative on the GRE.

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