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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] New post 27 Feb 2010, 23:09
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80% (01:06) correct 20% (00:00) wrong based on 2 sessions
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 :)



thanks in advance!
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Re: [HELP] OG 12 Question 97 & 98 DS [#permalink] New post 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 :)



thanks in advance!


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: [HELP] OG 12 Question 97 & 98 DS [#permalink] New post 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: [HELP] OG 12 Question 97 & 98 DS   [#permalink] 01 Mar 2010, 07:48
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