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number properties-OG (DS problem)

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Source: — Data Sufficiency |
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by papgust » Sun Mar 21, 2010 11:03 pm
x is -ve. Is x < -3?

1. x^2 > 9
x^2 - 9 > 0
(x+3) (x-3) > 0
x > 3 and x < -3 [In other words, x does not lie b/w -3 and 3]

We already know that x is -ve. So ignore x > 3.
x < -3. YES. Sufficient.

2. x^3 < -9
Say x=-3, x^3 = -27. -27 < -9. --> x = -3. NO
Say x=-4, x^3 = -64. -64 < -9. --> x < -3. YES
Insufficient.

IMO A
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by mitaliisrani » Sun Mar 21, 2010 11:14 pm
Thank you!
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by kstv » Mon Mar 22, 2010 12:14 am
If x is negative, is x<-3?
1) x^2 >9
2) x^3 <-9

2) x^3<-9 so x will be -ve even if if it is not given
cos only the cube of -ve number will give a value < 0
and x has to > -3 because (-3)^3 = -27
Since we know the range of x is it not Sufficient to say wheter x < -3 even if it is not in the affirmative.
What is the OE, please if you have it ?
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by papgust » Mon Mar 22, 2010 1:15 am
This problem is from OG12 Qn. #97.
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