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If x is positive, which of the following may be true?

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If x is positive, which of the following may be true?  [#permalink]

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New post 05 Aug 2019, 14:38
1
3
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

33% (01:45) correct 67% (02:13) wrong based on 48 sessions

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If x is positive, which of the following may be true?

I. x < x^2 < 1 + x
II. x < 1 - x < 2x
III. 1 - x < x < 1/x

A. 1 Only
B. 1 and 2
C. 1 and 3
D. 2 and 3
E. 1 2 and 3

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Re: If x is positive, which of the following may be true?  [#permalink]

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New post 07 Aug 2019, 04:01
How can option 2 may be correct? I have understood the point of 1 and 3
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Re: If x is positive, which of the following may be true?  [#permalink]

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New post 07 Aug 2019, 20:24
Hea234ven wrote:
How can option 2 may be correct? I have understood the point of 1 and 3


The answer to your question is that "X" can be a fraction.

For example with #2 when x=4/10, then 4/10<6/10<8/10

Same thing applies to number three but plug in 6/10 for X
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Re: If x is positive, which of the following may be true?  [#permalink]

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New post 07 Aug 2019, 20:52
Hello can someone please explain for II and III please ?
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Re: If x is positive, which of the following may be true?  [#permalink]

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New post 07 Aug 2019, 20:58
ctmerrill50 wrote:
Hea234ven wrote:
How can option 2 may be correct? I have understood the point of 1 and 3


The answer to your question is that "X" can be a fraction.

For example with #2 when x=4/10, then 4/10<6/10<8/10

Same thing applies to number three but plug in 6/10 for X



I have understood it.
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Re: If x is positive, which of the following may be true?  [#permalink]

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New post 07 Aug 2019, 23:03
TheNightKing wrote:
If x is positive, which of the following may be true?

I. x < x^2 < 1 + x
II. x < 1 - x < 2x
III. 1 - x < x < 1/x

A. 1 Only
B. 1 and 2
C. 1 and 3
D. 2 and 3
E. 1 2 and 3


For what value of x can I and III be true? Can someone please explain. I can see that II can be true for fractions.
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Re: If x is positive, which of the following may be true?  [#permalink]

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New post 07 Aug 2019, 23:12
1
We need not have a single value of x for all 3 statements; as long as x is positive. Try the values: 1.1, 0.49 and 0.51 for the three statements respectively.

If the answer is not E, please ignore the above reasoning and help me with an explanation instead!!! xD :P
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Re: If x is positive, which of the following may be true?  [#permalink]

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New post 08 Aug 2019, 11:04
If x is positive, which of the following may be true?

I. x < x^2 < 1 + x
II. x < 1 - x < 2x
III. 1 - x < x < 1/x


I. Substracting x
0<x^2-x<1
0<x(x-1)<1
For x=1.5 it is true

II. Adding x
2x<1<3x
x<1/2<3x/2
1/3<x<1/2
So for x=1/2.5=2/5 it is true

III. Adding x
1<2x<1/x + x
From the left: x>1/2
From the right, multipliyng by x (since we know that x is positive, there is no problem with the sign)
2x^2<1+x^2
x^2<1
-1<x<1
So, using both sides
1/2<x<1
Hence with x=3/4 it is true

Answer (E)
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Re: If x is positive, which of the following may be true?   [#permalink] 08 Aug 2019, 11:04
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