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If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 <

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If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 00:17
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If x is negative, is x <-3?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-is-negat ... 07229.html
[Reveal] Spoiler: OA

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Math Forum Moderator
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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 00:44
IEsailor wrote:
If x is negative, is x <-3?
(1) x^2 > 9
(2) x^3 < -9

(1) x^2>9
|x|>3
x>3 OR x<-3.
Not Sufficient.

(2) x^3<-9
The greatest value of x can be between -2 and -3.
-2^3=-8
-3^3=-27

So, x is definitely less than -2 but we don't know whether it is less than -3.
Not Sufficient.

Combining both we know x<-3.
Ans: "C"
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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 00:52
a gives |x| > 3 meaning regions x<-3 and x>3. not sufficient.

b gives x < 0. x < =-3 and -2<x<=-3. not sufficient.

a+b

C
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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 05:30
(1)
(x-3)(x+3) > 0

x < -3 or x > 3

(2)
x^3 < -9

x is -ve, but if x = -2.5

(-2.5)^3 < -9, but x > -3

(1) + (2)

x < -3

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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 08:09
1
KUDOS
1)
$$x<-3$$ and $$x>3$$,
we are given that $$x<0$$, so only $$x<-3$$ holds true, sufficient

2)
$$x<-2.2$$ (it's estimation of $$\sqrt[3]{9})$$, not sufficient.

(A)

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Math Forum Moderator
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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 08:38
1
KUDOS
ulm wrote:
1)
$$x<-3$$ and $$x>3$$,
we are given that $$x<0$$, so only $$x<-3$$ holds true, sufficient

2)
$$x<-2.2$$ (it's estimation of $$\sqrt[3]{9})$$, not sufficient.

(A)

True!!! Thanks!!!
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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 12:28
I also missed that x is negative in the question steam. Thanks for pointing out.

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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 13:16
from stmnt (2) x.x.x<-9
if x=-3 , x.x.x=-27 ,-27<-9 , -3>-3 the answer is no
if x=-4 ,x.x.x=-64, -64<-9 , -4>-3 the answer is no
by taking different values we can conclude that x is not greater than -3.

by taking x=-2, x.x.x=-8, -8 is not less than -9 ,which makes statement (2) false.

Is my above reasoning correct. plz explain

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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 13:40
TomB wrote:
from stmnt (2) x.x.x<-9
if x=-3 , x.x.x=-27 ,-27<-9 , -3>-3 the answer is no
if x=-4 ,x.x.x=-64, -64<-9 , -4>-3 the answer is no
by taking different values we can conclude that x is not greater than -3.

by taking x=-2, x.x.x=-8, -8 is not less than -9 ,which makes statement (2) false.

Is my above reasoning correct. plz explain

What if x=-2.5. Nowhere it's mentioned that x must be an integer.
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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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19 May 2011, 15:40
Good point there @ulm.

1. Sufficient

as x<-3

2. Not sufficient

x^3<9

=> x may or may not be less than -3.

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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 < [#permalink]

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29 Nov 2017, 00:47
If x is negative, is x < –3 ?

(1) x^2 > 9 --> $$x<-3$$ or $$x>3$$ as given that $$x<0$$ then we have that $$x<-3$$. Sufficient.

(2) x^3 < –9 --> if $$x=-3$$ ($$x^3=-27<-9$$) then the answer will be NO (as $$x$$ equals to -3 and is not less than -3) but if $$x=-4$$ ($$x^3=-64<-9$$) then the answer will be YES. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-is-negat ... 07229.html
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Re: If x is negative, is x <-3? (1) x^2 > 9 (2) x^3 <   [#permalink] 29 Nov 2017, 00:47
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