Inequalities

I am sure u got to determining each statement individidually is not sufficient

2x-2y = 1

x-y = 1/2

x/y>1

Multiply both sides of x/y>1 by y^2 (doesn not change the inequality since y^2 is always positive based on given statements i.e. can't be 0)

y^2 x/y>y^2

xy>y^2

xy-y^2>0
y(x-y) >0

We know x-y=1/2 a positive quantity therefore y cant be negative. y is positive and therefore x is positive (since x-y=1/2)


C

wow! I can see Ian's signature steps in CR's solution.

Stmt 1: x-y = 1/2
it says x = y+1/2
so x and y may be both positive both negative one positive another negative vice versa... depending on values of y

2. says x/y > 1
again x and y both can be positive or negative x=2, y=1 x/y>1
x=-2, y=-1, x/y>1

Note the sign cant be different as that way the no will be negative.

combining: we know x>y from 1, and from 2 we know the number must be bigger in magnitude but -2<-1 so both must be positive

C