Is x y ? (1) x^2 2y (2) x^3 y^4

Question

Is x > y ?

(1) x^2 > 2y

(2) x^3 > y^4

chetan2u · Answer

(1) x^2 > 2y If x<0, we can have both possibilities. x=-3 and y=-2.......y>x x=-3 and y=-4.......x>y If x>0, again both possibilities x=1, y=1/3....x>y x=4, y=7.....y>x Rather 0x^2 , so x>x^2>2y or x>y Insufficient (2) x^3 > y^4 This tells us that x is positive. If x>1 , then x^3 > y^4........x>y^{\frac{4}{3}}>y If x<1, then x^3 > y^4........x^{\frac{3}{4}}>y .. But x^{\frac{3}{4}}>x WHY? Because value decreases with increase in power and vice versa. So, x^{\frac{3}{4}}>y>x or x^{\frac{3}{4}}>x>y Insufficient Combined We know x is positive from statement II. Case I: 0y from statement I. Case II: x>1........x>y from statement II. Thus, both statements are satisfied only when x>y. Sufficient C

stoned · Answer

hi  chetan2u ,
I didn't understand how we deduce this highlighted part. Can you elaborate a bit, please?
Thanks

Is x > y ? (1) x^2 > 2y (2) x^3 > y^4

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