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Algebraic Solution needed

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Algebraic Solution needed

by smackmartine » Mon Oct 10, 2011 8:58 pm
Hi guys,
Sometimes under time pressure I am not able to think appropriate fractions or #s when it comes to inequalities.
While solving sufficiency for individual statements I can quickly test the sufficiency, but when it comes to combining both statement I either mess up or it takes me longer than I should. However, I can almost do any algebra on a fly. Please suggest an algebraic method to solve combined statement 1 and 2.

OA C

Is x > y?

(1) sqrt(x) > y

(2) x^3 > y
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by cans » Mon Oct 10, 2011 9:43 pm
x>y??
B) x^3 >y
x=2, y=3. b) satisfies but x<y and x=10,y=3 satisfies both condition. Insufficient

A) root(x) > y
if x=1/4, sqrt(x)=1/2. if y>1/4 and y<1/2, only one condition will satisfy. Thus insufficient

A&B) x <0 is not possible as sqrt (x)>0 is given. if y<0, then all conditions satisfy. x>y also.
Now if x>1, and sqrt(x) >y, then x>y is true.
and when x<1, x^3 <x and y<x^3 thus y<x
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by smackmartine » Mon Oct 10, 2011 9:52 pm
cans wrote:x>y??
A&B) x <0 is not possible as sqrt (x)>0 is given. if y<0, then all conditions satisfy. x>y also.
Now if x>1, and sqrt(x) >y, then x>y is true.
and when x<1, x^3 <x and y<x^3 thus y<x
This is what I was looking for. :D
Thanks !
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