Inequality

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Fri May 08, 2009 10:27 pm

1. -2x > 0 - you have a negative number multiplied by x to get a positive number (since -2x is positive). This means that x must also be negative, since, if x were positive, then (negative)*(positive) <0.
So 1 is sufficient.

2. Consider this: x^3 = (x^2)*x. x^2 will always be positive or equal to zero, so the sign of (x^2)*x (or x^3, as you prefer) will always be set by x.
If x is positive, then (x^2)*x = (positive)(positive) = positive.
If x is negative, then (x^2)*x = (positive)(negative) = negative.
Since x^3 < 0, then x will "follow" the sign: x < 0.
So 2 is sufficient as well.

The point made with statement 2 can be expanded into a nice little rule:

No matter the sign of x, x raised to an even power will always be positive or equal to zero (if x = 0).

Odd powers of x will share the sign of x. If x is positive, then x raised to an odd power will also be positive. If x is negative, then x raised to an odd power will also be negative.

Got it.

Last edited by DanaJ on Sat May 09, 2009 8:33 am, edited 1 time in total.

Quote

chetanojha: Master | Next Rank: 500 Posts; Posts: 125; Joined: Sun Sep 16, 2007 1:38 pm; Thanked: 6 times

by chetanojha » Sat May 09, 2009 3:57 am

Thanks Guys. This question was from Quant Review. I got the concept now.

Quote

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Sat May 09, 2009 8:12 am

Odd powers of x will share the sign of x. If x is positive, then x raised to an odd power will also be positive

.

TRUE

If x is negative, then x raised to an even power will also be negative.

Not true.

Probably u meant to say

If x is negative, then x raised to an odd power will also be negative

If x is negative or positive x raised to an even power will always be positive.

Regards,
CR