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Number properties question

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Source: — Problem Solving |
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by cramya » Mon May 18, 2009 8:52 pm
u,v-> positive real numbers

Stmt I

u^3< v

u=2 v=10000000 U>V NO

u=1/2 v=1/4 YES

INSUFF

Stmt II

u^1/3 < v

Cube both sides

u < v^3

u=10 v=9 YES

u=1 v=1000000 NO

INSUFF

Together:

u^3<v
u<v^3

Add inequalities facing same direction

u^3+u < v+v^3

u(u^2+1) < v(v^2+1)

u has to be less than v since u and v are given to be positive


Choose C
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by KICKGMATASS123 » Tue May 19, 2009 5:27 pm
cramya wrote:u,v-> positive real numbers

Stmt I

u^3< v

u=2 v=10000000 U>V NO

u=1/2 v=1/4 YES

INSUFF

Stmt II

u^1/3 < v

Cube both sides

u < v^3

u=10 v=9 YES

u=1 v=1000000 NO

INSUFF

Together:

u^3<v
u<v^3

Add inequalities facing same direction

u^3+u < v+v^3

u(u^2+1) < v(v^2+1)

u has to be less than v since u and v are given to be positive


Choose C
Awesome explaination Cramya.. You rock!! ;)
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