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If -1 < x < 1, and x ≠ 0, which of the following inequalities must be

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Joined: 02 Sep 2009
Posts: 52210
If -1 < x < 1, and x ≠ 0, which of the following inequalities must be  [#permalink]

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08 May 2016, 22:40
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If -1 x^4
III. x^3 > x^5

A. I only
B. I and II
C. II only
D. II​ and III
E. I, II, and III

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If -1 < x < 1, and x ≠ 0, which of the following inequalities must be  [#permalink]

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08 May 2016, 23:07
I. x^3 < x^4 fails when x = 1/2
II. x^2 > x^4 100 % true in all case
III. x^3 > x^5 fails when x=-1/2

So in my IMO : C
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Joined: 11 Aug 2013
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If -1 < x < 1, and x ≠ 0, which of the following inequalities must be  [#permalink]

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08 May 2016, 23:15
1
Bunuel wrote:
If -1 < x < 1, and x ≠ 0, which of the following inequalities must be true?

I. x^3 < x^4
II. x^2 > x^4
III. x^3 > x^5

A. I only
B. I and II
C. II only
D. II​ and III
E. I, II, and III

C I think.

Take for any example any fraction and plug that in :-

for stmt 1 :- take x = -1/2
- 1/8 < 1/16 which is true
x = 1/2
1/8 > 1/16 hence not true
stmt 2 : - both the quantitienties x^ 2 and x^4 will be positive
and 1/4 > 1/16 which will be true for any fraction
stmt 3 :- x3 > x^5 will not be true for negative fractions
-1/8 < -1/32
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Re: If -1 < x < 1, and x ≠ 0, which of the following inequalities must be  [#permalink]

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10 May 2016, 04:56
Bunuel wrote:
If -1 < x < 1, and x ≠ 0, which of the following inequalities must be true?

I. x^3 < x^4
II. x^2 > x^4
III. x^3 > x^5

A. I only
B. I and II
C. II only
D. II​ and III
E. I, II, and III

Ans:-

Given :- -1<x<0 and 0<x<1 means all fractions in between .

Must be true.

I. if x = -1/2 (true) but if x =1/2 (false) eliminate it.
II. Generally irrespective of signs all even powers will be positive and if power is greater value also will be greater for integers but for fractions it is reverse.
ex:- test for x =1/2 or -2/3 and so on.
This option Holds good

III. odd powers this statement is false for all positive numbers and true for all negatives.

for fractions if x= 1/2 (true) but for x=-1/2 (false) eliminate.

SO only II must be true . Ans is [b} C[/b]
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Re: If -1 < x < 1, and x ≠ 0, which of the following inequalities must be  [#permalink]

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10 May 2016, 07:48
Bunuel wrote:
If -1 < x < 1, and x ≠ 0, which of the following inequalities must be true?

I. x^3 < x^4
II. x^2 > x^4
III. x^3 > x^5

A. I only
B. I and II
C. II only
D. II​ and III
E. I, II, and III

Plug in some values of x

Say $$x$$ $$=$$ $$1/2$$

Now check the options

I. x^3 < x^4

$${1/2}^3$$ < $${1/2}^4$$ => $$\frac{1}{8} > \frac{1}{16}$$

II. x^2 > x^4

$${1/2}^2$$ > $${1/2}^4$$ => $$\frac{1}{4} > \frac{1}{16}$$

III. x^3 > x^5

$${1/2}^3$$ < $${1/2}^5$$ => $$\frac{1}{8} < \frac{1}{32}$$

Hence we find that only option C. II satisfies the given condition...
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Re: If -1 < x < 1, and x ≠ 0, which of the following inequalities must be  [#permalink]

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11 Jul 2018, 08:09
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Re: If -1 < x < 1, and x ≠ 0, which of the following inequalities must be &nbs [#permalink] 11 Jul 2018, 08:09
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