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chetanojha
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2) x^3<0 => if x^3 <0, then x has to be negative.
D.
This is what came to my mind, I am not expert
Somebody, please explain.
Thanks
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Source: Beat The GMAT — Data Sufficiency |
1) -2x>0 => 2x< 0 => x<0
2) x^3<0 => if x^3 <0, then x has to be negative.
D.
This is what came to my mind, I am not expert
Somebody, please explain.
Thanks
2) x^3<0 => if x^3 <0, then x has to be negative.
D.
This is what came to my mind, I am not expert
Somebody, please explain.
Thanks
Could you please confirm statement-2?
chetanojha wrote:How can we solve this.
Is x<0?
1. -2x>0
2. x^3<0
OA: D
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.
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.
.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
Positive number with Odd power will always positive.
Negative number with Odd power will always negative.
So if x^3<0 then it is negative.
Negative number with Odd power will always negative.
So if x^3<0 then it is negative.
