Question

consider the integers x and y, when y is divided by x the remainder is 29. when y is divided by x/2 the remainder is 13. determine x

Answer 1

Answer:

If x and y are integer, what is the remainder when x^2 + y^2 is divided by 5?

(1) When x-y is divided by 5, the remainder is 1 --> , so can be 1, 6, 11, ... Now, and () then and thus the remainder is 0, but if and () then and thus the remainder is 3. Not sufficient.

(2) When x+y is divided by 5, the remainder is 2 --> , so can be 2, 7, 12, ... Now, and () then and thus the remainder is 2, but if and () then and thus the remainder is 4. Not sufficient.

(1)+(2) Square both expressions: and --> add them up: --> so is divisible by 5 (remainder 0), which means that so is . Sufficient.

Answer: C.

Hope it's clear.

Step-by-step explanation:

Mark as brilliant