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inequalities

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inequalities

by ketkoag » Mon Mar 30, 2009 8:34 am
If x is negative, is x < -3?
(1) x^2 > 9
(2) x^3 < -9
OA: A
my answer is C.

General question: if x>1, x<-1, and x<0 then is x<-1?? Coz i feel that it is true. please expalin if i am wrong.
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by rs2010 » Mon Mar 30, 2009 9:38 am
A says

X^2>9
X^2-9>0
(X-3) ( X+3)> 0

for ineq to be positive

either both the terms should be less than 0 or both should be greater than 0.

X-3>, X+3>0 ; X-3<0 X+3<0
X>3 X>-3 ; X<3 X<-3

If X>3 then there no use of X>-3 and since X is negative so leave this

since X<-3 so leave X<3.. and this is what we wanted


B is crappy

X is less than cube root of -9 which it can take value greater and less than -3. eg. -2.1 to -2.9 and beyond -3
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by cm47323 » Mon Mar 30, 2009 9:38 am
(1) x > 3 or x < -3, since we know x is negative, sufficient
(2) x < -9^(1/3) . approximately x < -2.1, insufficient

A
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by ketkoag » Mon Mar 30, 2009 10:41 am
General question: if x>1, x<-1, and x<0 then is x<-1?? Coz i feel that it is true. please expalin if i am wrong.
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by mike22629 » Mon Mar 30, 2009 11:51 am
Yes, if you divide an inequalities by a negative number the crocodile changes directions hence:

if X>1, then -X<-1
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by mike22629 » Mon Mar 30, 2009 11:53 am
Yes, if you divide an inequalities by a negative number the crocodile changes directions hence:

if X>1, then -X<-1
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