If x 0 and y 0, is y^3 x^2? (1) y x (2)

Question

If x > 0 and y > 0, is y^3 > x^2?

(1) y > x
(2) y^2 > x

Sorry, it y^2 and y2...

twixt · Answer

I pick C.

Even if we do not have enough data to enough whether x and y are >1 or <1, combined statements involve that (x and y being >0) y2.y>x.y>x.x

vprabhala · Answer

my Bad... its C.. inequalities help..!

oxon · Answer

C too. It took me a while though.

foraj · Answer

I would go with c. using fractions and some integers.

ninomoi · Answer

Can someone pls explain this? :cry:

gayathri · Answer

ninomoi,

This is how I would do this.

Stem: x>0, y>0 ie x & y are positive

s : y>x
Let y=3, x=2; y^3=27 and x^2=4, so y^3 IS greater than x^2 (y^3>x^2)
Let y=1/3, x=1/4; y^3=1/27, x^2=1/16, so y^3 IS NOT greater than x^2 (y^3 x
Let y=4, x=3, y^2>x (16>3); y^3=64 and x^2=9, so y^3 IS greater than x^2 (y^3>x^2)
Let y=2, x=3, y^>x (4>3); y^3=8 and x^2=9, so y^3 IS NOT greater than x^2 (y^3 x => xy>x^2 ---->(a)
(we can multiply by a positive number and retain the inequality) 
Similarly, y^2>x => y^3>xy>x^2 -----> from (a)

ie, y^3>x^2

S +s  is sufficient. C

If x > 0 and y > 0, is y^3 > x^2? (1) y > x (2)

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