## For all integers $$a$$ and $$b,$$ the operation $$\theta$$ is defined by $$a\theta b=\dfrac{a+b}2.$$ If $$x$$ and $$y$$

##### This topic has expert replies
Legendary Member
Posts: 1486
Joined: 01 Mar 2018
Followed by:2 members

### For all integers $$a$$ and $$b,$$ the operation $$\theta$$ is defined by $$a\theta b=\dfrac{a+b}2.$$ If $$x$$ and $$y$$

by Gmat_mission » Fri Aug 20, 2021 11:39 am

00:00

A

B

C

D

E

## Global Stats

For all integers $$a$$ and $$b,$$ the operation $$\theta$$ is defined by $$a\theta b=\dfrac{a+b}2.$$ If $$x$$ and $$y$$ are integers, is $$x\theta y$$ an integer?

(1) $$x^2=y^2$$

(2) $$x=-y$$