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whether x is greater than 0? 1)x^2>x^3 2) x^3<x^4

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whether x is greater than 0? 1)x^2>x^3 2) x^3<x^4 [#permalink]  28 Sep 2004, 06:43
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332. DS: whether x is greater than 0?
1)x^2>x^3Â Â
2) x^3<x^4
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C it is
1) x can be a fraction or negative
2) x can be positive integer > 1 or negative

Both combined we know x is negative
Remember what exponents do to numbers when
<-1
-1 to 0
0 to 1
>1
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Paul

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I think E.

1. X^2-X^3>0 =>X^2(1-X)>0 =>X<1 or X<0 or X>0. So, Insuff.

2. X^3-X^4<0 =>X^3(1-X)<0 =>X>1 or X<0. So, Insuff.

Combining both we still have many possibilities of X. Hence E.
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Anonymous wrote:
I think E.

1. X^2-X^3>0 =>X^2(1-X)>0 =>X<1 or X<0 or X>0. So, Insuff.

2. X^3-X^4<0 =>X^3(1-X)<0 =>X>1 or X<0. So, Insuff.

Combining both we still have many possibilities of X. Hence E.

For #1, x cannot be >0
For instance, 2 would not work. x would have to be a positive fraction or any negative number. I stand by C
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Paul

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Guest...

if both the equations were to be true ( put together) then the only possibility is x<0 n hence it shud be C....
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[quote="Paul"]C it is
1) x can be a fraction or negative
2) x can be positive integer > 1 or negative

Both combined we know x is negative
Remember what exponents do to numbers when
<-1
-1 to 0
0 to 1
>1[/quote
Paul can you please elaborate the rule about what exponent do to the number?
S
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Let's take the example of x^n where n is an integer >1

when x<-1, and n is even, result will be positive; when n is odd, result will be negative. As n goes up, the abs val of the expression will be larger and larger. This is the property of integers >1 or >-1
when x is b/w -1, 0 and n is even, fraction will be positive; when n is odd, result will be a negative fraction. As n goes up, the abs val of the expression will be smaller and smaller. This is the case with fractions as you increase the exponent.
when x is b/w 0, 1, the greater n, the smaller the fraction
when x is>0, the greater n, the larger the expression.
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Paul

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To me

statement 1 : x<1
statement 2 : Abs(x)>1

1+2 : x<-1 id est x < 0

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Paul wrote:
C it is
1) x can be a fraction or negative
2) x can be positive integer > 1 or negative

Both combined we know x is negative
Remember what exponents do to numbers when
<-1
-1 to 0
0 to 1
>1

1) positive fraction < 1, negative numbers
2) negative numbers, positive numbers > 1

so if negative is the correct answer then would the right choice for this be:

Is the vehicle a 4x4?
1) 4x4 truck, boat
2) 4x4 suv, boat

can only be a boat?
dont mean to oversimplify just trying to come up with right analogy.
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Anonymous wrote:
I think E.

1. X^2-X^3>0 =>X^2(1-X)>0 =>X<1 or X<0 or X>0. So, Insuff.

2. X^3-X^4<0 =>X^3(1-X)<0 =>X>1 or X<0. So, Insuff.

Combining both we still have many possibilities of X. Hence E.

Wrong because when X^2(1-X)>0 , since X^2 >= 0 always hence 1-X > 0
therefore X < 1 is all that can be derived from the statement.

C is the right answer as explained well above.
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