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If x^4 > x^5 > x^3, which of the following could be the value of x?

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If x^4 > x^5 > x^3, which of the following could be the value of x?  [#permalink]

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New post 23 Feb 2016, 03:05
1
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:20) correct 19% (01:11) wrong based on 183 sessions

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Math Expert
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If x^4 > x^5 > x^3, which of the following could be the value of x?  [#permalink]

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New post 23 Feb 2016, 08:28
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1
Bunuel wrote:
If x^4 > x^5 > x^3, which of the following could be the value of x?

A. -3
B. -2
C. -2/3
D. 2/3
E. 3


Kudos for correct solution.


Hi,
this Q tests us on our concepts on Number properties..
x^4 > x^5 > x^3
1)here we have even power of a variable and it is more than both a bigger odd power and smaller odd power..
It can be possible only if the base is negative so x is -ive..
2) Now if x is negative, a higher power means a smaller number, if x<-1..
and a higher power results in a bigger number if 0>x>-1

combined we know that x is a negative number greater than -1..

only -2/3 is in the choices..
ans C


SUBSTITUTE
Ofcourse we can substitute each value given in choice and find answer

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If x^4 > x^5 > x^3, which of the following could be the value of x?  [#permalink]

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New post 23 Feb 2016, 09:47
Bunuel wrote:
If x^4 > x^5 > x^3, which of the following could be the value of x?

A. -3
B. -2
C. -2/3
D. 2/3
E. 3


Kudos for correct solution.


Let's break this question down into two parts. I: \(x^4 > x^5\) and II: \(x^5 > x^3\)
Consider Part I:
\(x^4 > x^5\)
For this to be true, either \(x\) is negative or it is a fraction less than 1

Consider Part II:
\(x^5 > x^3\)
If \(x\) is negative, then for this to be true, \(x\) has to be greater than -1.
If \(x\) is a fraction less than 1, then for this part to be true, \(x\) must also be negative.

In either case, \(x\) can be represented by the inequality \(0>x>-1\).
The only option that satisfies this condition is C (-2/3)
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Re: If x^4 > x^5 > x^3, which of the following could be the value of x?  [#permalink]

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New post 01 Apr 2016, 18:37
Bunuel wrote:
If x^4 > x^5 > x^3, which of the following could be the value of x?

A. -3
B. -2
C. -2/3
D. 2/3
E. 3


Kudos for correct solution.


consider all three cases saperatly
a> x^4>x^3
b> x^5>x^3
c>x^4>x^5

a> x^4-x^3>0------>x^2-x>0------->x>1 or x<0
b> x^3-x>0---------->x>1 or -1<x<0
c> x^4-x^5>0-------> x^5-x^4<0-------->x-1<0------>x<1

intersection point of all three ranges are -1<x<0
only option C satisfies the criteria
So ans C.
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Re: If x^4 > x^5 > x^3, which of the following could be the value of x?  [#permalink]

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New post 29 Jan 2018, 10:39
Bunuel wrote:
If x^4 > x^5 > x^3, which of the following could be the value of x?

A. -3
B. -2
C. -2/3
D. 2/3
E. 3


We are given that x^4 > x^5 > x^3.

Since x^4 is greater than x^5, we see that x cannot be a positive integer.

Since x^5 is greater than x^3, we see that x cannot be a negative integer or a positive proper fraction.

Thus, x must be -2/3.

Answer: C
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Re: If x^4 > x^5 > x^3, which of the following could be the value of x?   [#permalink] 29 Jan 2018, 10:39
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