If x 0 and y 0, is y3 x2? (1) y x (2) y2 x

Question

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

(1)  y > x

(2)  y^2 > x

philipssonicare · Answer

(1) y>x 2>1 2^3 and 1^2 8>1 But, the original condition indicates both x and y are positive, not that they are integers. 0.2>0.1 0.2^3 and 0.1^2 0.008<0.01 Insufficient (2) y^2 >x 2^2 >1 4>1 2^3 and 1^2 8>1 but 2^2 >3 4>3 2^3 and 3^2 8<9 Insufficient Together: y>x and y^2 >x Now, combine the two inequalities (knowing that all values are positive) y· y^2 >x·x y^3 > x^2 Sufficient C

rahul16singh28 · Answer

Individually, Option A & B are not sufficient as x, y can be Integer or fraction.

By multiplying both option we get -

y^3 > x^2

Hence, C.

Mo2men · Answer

Dear  GMATGuruNY

Can you share your way of solution in such question? is safe to multiply both statements as long as variables positives? if yes, could not fraction values affect the multiplication?

Thanks in advance

GMATGuruNY · Answer

If  a>b  and  c>d , and all of the values are positive, then  ac>bd .
Combining the two statements:
Since  y>x  and  y^2>x , and  x  and  y  are both positive,  y^3>x^2 .
SUFFICIENT.

C

bumpbot · Answer

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If x > 0 and y > 0, is y3 > x2? (1) y > x (2) y2 > x

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