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

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If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9 [#permalink]  27 Feb 2010, 23:09
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If x is negative, is x < –3 ?

(1) x^2 > 9
(2) x^3 < –9

[Reveal] Spoiler:
My initial answer was D (either one is sufficient). but the books says the correct answer is A (Statement 1 alone is sufficient)

I could understand the explaination that was offered for 1) but not for 2)

Explaination for 2)
Given that x^3 < -9 if x = -4 , then x^3 = - 64. so x^3<-9. and it is true than x <-3. However if x = -3 (this is the part i don't get), then x^3 = -27 and so x^3 <-9 but it is not true that x<-3, NOT SUFFICIENT

What does this mean?? Why are we even considering x=-3 when the question clearly says that x<-3 (therefore the value should be anything less than -3 (Eg -10, -8, -4 etc.).

Clarification much needed

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-is-negative-is-x-107229.html
[Reveal] Spoiler: OA
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Re: If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9 [#permalink]  28 Feb 2010, 01:37
acedemania wrote:
Hi guys, I'm having abit of a problem trying to comprehend the explaination given by the OG guide on Question 97 DS.

If x is negative, is x<-3

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

My initial answer was D (either one is sufficient). but the books says the correct answer is A (Statement 1 alone is sufficient)

I could understand the explaination that was offered for 1) but not for 2)

Explaination for 2)
Given that x^3 < -9 if x = -4 , then x^3 = - 64. so x^3<-9. and it is true than x <-3. However if x = -3 (this is the part i don't get), then x^3 = -27 and so x^3 <-9 but it is not true that x<-3, NOT SUFFICIENT

What does this mean?? Why are we even considering x=-3 when the question clearly says that x<-3 (therefore the value should be anything less than -3 (Eg -10, -8, -4 etc.).

Clarification much needed

Here, it is asking whether x<-3 or not, it's not an information rather it's being asked. As far as explanation for letting x=-3 is concerned, when you take x=-3 then x^3=-27 that means for the given information x^3<-9 to be true x can be either x=-3 or x<-3 for values of x=-4 onwards, so from the given information x^3<-9 we can't exactly say whether x<-3 or not, it's not sufficient because it can be either x<-3 or x=-3 so not sufficient. If it was asked "is x<=-3" then the information II x^3<-9 was sufficient.

Hope it helps!
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Re: If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9 [#permalink]  01 Mar 2010, 07:48
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Ans A

Using (1)
x^2>9 => x^2 - 9>0 => (x-3)(x+3)>0 => x>3 or x<-3

It is already given x is negative , so x<-3

SUFFICIENT

Using (2)
x^3 < -9
x < (-9)^1/3 [(-8)^1/3 = -2, so (-9)^1/3 must be around -2.1]
=> x < -2.1

INSUFFICIENT
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Re: If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9 [#permalink]  02 Jan 2015, 17:19
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Re: If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9 [#permalink]  05 Jan 2015, 02:51
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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: if-x-is-negative-is-x-107229.html
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Re: If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9   [#permalink] 05 Jan 2015, 02:51
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