Is x y ? (1) xa ya (2) x − a y − a

Question

Is x > y ?

(1) xa > ya
(2) x − a > y − a

chetan2u · Answer

Is x > y ?

(1) xa > ya
xa-ya>0……….(x-y)a>0
Depends on the sign of a as +*+>0 or -*->0
If a>0, then x-y>0 or x>y.....2*1>1*1
If a<0, then x-y<0 or x<y.....2*-1>3*-1

(2) x − a > y − a
Add a to both sides to get x>y.
Sufficient

B

Romik · Answer

Why can't we subtract both sides by a in the first case (like you say to add a to both sides in the second)?

chetan2u · Answer

You can but it will not affect the equation or simplify the equation. 
xa>ya…….xa-a>ya-a
Yes you could take both on the same side. 
xa>ya……xa-ya>0……..a(x-y)>0

Romik · Answer

I'm sorry, I meant - why can't we divide both sides by a?

Is x > y ? (1) xa > ya (2) x − a > y − a

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