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## Good inequality...

amit.trivedi@ymail.com GMAT Destroyer!
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Good inequality... Mon May 07, 2012 1:30 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
"If x is negative, is x < -3 ?

(1) x^2 > 9
(2) x^3 < -9 "

I donot have the OA but when I solved the question, I got the answer as E.

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aneesh.kg GMAT Destroyer!
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Mon May 07, 2012 1:53 am
Statement (1):
x^2 - 9 > 0
Using critical points method for x < 0
x < -3
(You will get the same answer even by plugging-in numbers)
SUFFICIENT

Statement(2):
x^3 + 9 < 0
Plug-in negative values. The inequality does not hold true for -1 and -2. It holds true first when x^3 = - 9.
x = - (9)^1/3
Since (-2)^3 = - 8 and (-3)^3 = - 27, and
-27 < - 9 < - 8,
x is between -2 and -3 and slightly less than - 2.
x = - 2.1 (approx)
Below this value, the statement will always hold true.

x < - 2.1

i.e., x can be less than - 3 or even greater than it (for the values between - 2.1 and - 3).

INSUFFICIENT.

Traps in this problem:
(1)The problem does not mention that x is an integer, so some people will fall into the trap of assuming x as an integer and go with (D)
(2) x is negative. If you don't notice this you will go with (C).

What is the Critical Points method?
http://www.beatthegmat.com/critical-points-method-for-inequalities-explained-useful-t110450.html#465861

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Anurag@Gurome GMAT Instructor
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Tue May 08, 2012 9:39 pm
amit.trivedi@ymail.com wrote:
"If x is negative, is x < -3 ?

(1) x^2 > 9
(2) x^3 < -9 "

I donot have the OA but when I solved the question, I got the answer as E.
(1) x² > 9 implies x < -3 or x > 3
It is given that x is negative or x < 0, so x < -3; SUFFICIENT.

(2) x^3 < -9
If x = -3, then x^3 = -27. Here x is equal to -3 and not less than -3.
If x = -4, then x^3 = -64. Here x < -3.

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