X range is -1 <X <1, Q Which of the following must be true?
Answers are:
X ^ 2> X ^ 3,
(X +1 / 2) (X-1 / 2) <0
Answers are:
X ^ 2> X ^ 3,
(X +1 / 2) (X-1 / 2) <0
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Which is correct?
Source: Beat The GMAT — Problem Solving |
I guess X ^ 2> X ^ 3 is also not true when X = 0 . Please let me know if I am missing anything ?
Solution.
Obviously x^2 > x^3 does not hold for x = 0.
Taking the second statement we have that (X +1 / 2) (X-1 / 2) <0
So we have that either (a) (X +1 / 2)>0 and (X-1 / 2)< 0
Or
(b) (X +1 / 2)<0 and (X-1 / 2)>0. This would mean x<-1/2 and x>1/2 which is not possible and so (b) is automatically rejected.
So we have that (X +1 / 2) (X-1 / 2) <0 implies -1/2<x<1/2 which is possible because given range of x is -1 <x<1.
The second statement is true.
Obviously x^2 > x^3 does not hold for x = 0.
Taking the second statement we have that (X +1 / 2) (X-1 / 2) <0
So we have that either (a) (X +1 / 2)>0 and (X-1 / 2)< 0
Or
(b) (X +1 / 2)<0 and (X-1 / 2)>0. This would mean x<-1/2 and x>1/2 which is not possible and so (b) is automatically rejected.
So we have that (X +1 / 2) (X-1 / 2) <0 implies -1/2<x<1/2 which is possible because given range of x is -1 <x<1.
The second statement is true.
Rahul Lakhani
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Gurome, Inc.
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
first statement doesnt hold always put x=0
for second statement x should be between -1/2 and 1/2.since range of x is between -1 and 1.so it is always true.
quantskillsgmat
wisdommart delhi
for second statement x should be between -1/2 and 1/2.since range of x is between -1 and 1.so it is always true.
quantskillsgmat
wisdommart delhi
