Operating Evens!

Level 1

The addition, subtraction, product, and division between 2 positive integers are known to be all even.

Let X represent the larger of the 2 numbers and Y represent the smaller of the 2 numbers.

Which of the following options is correct?

X must be a multiple of 4 Both X and Y must be a multiple of 4 Y must be a multiple of 4 Either X or Y must not be a multiple of 4

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1 solution

X X
Nov 7, 2018

If X + Y X+Y is even, so X Y ( m o d 2 ) X\equiv Y\pmod2

X Y XY is even, so one of X X and Y Y must be even.

So, both of them are even. Let X = 2 x , Y = 2 y X=2x,Y=2y

X Y = x y \frac XY=\frac xy is an even number, so x x is even, 2 x 2x is a multiple of 4.

Hence, X X must be a multiple of 4, and Y Y must be an even number.

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