OG Page 290, # 154 - need faster method

[jaydeer44]

Is there an easy way to solve this problem? The OG explanation basically says to plug in numbers for each equation to come up with a range of numbers that satisfies both (1) and (2), but that takes way too long!

The answer is C.

154. Is x negative?

(1) x^3 (1 - x^2) < 0
(2) x^2 - 1 < 0

[musicdaemon]

Analyse the first option:

Case I:
x^3 (1 - x^2) <0>1
i.e. x^2-1>0 ...................... this condition is not supplied in the question

Case II:
x^3 = -ve, then (1-x^2) must be +ve
The necessary and sufficient condition for (1-x^2) to be +ve, is
x^2<1
i.e x^2-1<0 .......... Which is the conditon supplied in statement 2

thus c should be the answer

[musicdaemon]

Case I:
for, x^3 (1 - x^2) <0>1[/b]
i.e. x^2-1>0 ...................... this condition is not supplied in the question

[musicdaemon]

Case I:
for, x^3 (1 - x^2) <0>1[/b]
i.e. x^2-1>0 ...................... this condition is not supplied in the question

MODS,
There is some problem in formatting of this part, not able to paste it properly.

anyway case 2 suffices my explanation

[Stuart@KaplanGMAT]

Case I:
for, x^3 (1 - x^2) <0>1[/b]
i.e. x^2-1>0 ...................... this condition is not supplied in the question

MODS,
There is some problem in formatting of this part, not able to paste it properly.

anyway case 2 suffices my explanation

HTML is the devil!

HTML uses < > for its tags, so if you have HTML turned on you'll often have formatting issues on inequality questions.

If you click the "Disable HTML in this post" box, your problems will disappear. You can either do so for particular posts or you can change the setting permanently in your profile - change "Always allow HTML" from "yes" to "no" (that's what I've done, since BBCode accomplishes the same thing as HTML and doesn't cause the same issues to arise).

[gabriel]

Yup, whatever Stuart said..