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If x is positive, which of the following may be true?
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Updated on: 01 Oct 2019, 15:11
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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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Originally posted by TheNightKing on 05 Aug 2019, 13:38.
Last edited by TheNightKing on 01 Oct 2019, 15:11, edited 1 time in total.



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Re: If x is positive, which of the following may be true?
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07 Aug 2019, 03:01
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?
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07 Aug 2019, 19:24
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?
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07 Aug 2019, 19:52
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?
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07 Aug 2019, 19:58
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?
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07 Aug 2019, 22:03
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?
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07 Aug 2019, 22:12
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?
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08 Aug 2019, 10:04
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^2x<1 0<x(x1)<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?
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07 Sep 2019, 06:13
I. x < x^2 < 1 + x Subtracting X across the inequation, 0 < X^2  X < 1 = 0 < X (X1) < 1...….X (X1) will be less than 1 when X1 is less than one. Hence this equation is true for all values of X from 1.1 to 1.9. Hence TRUE
II. x < 1  x < 2x We can split it in two parts. Firstly, X < 1X and secondly 1X < 2X X < 1X which gives X < 1/2 1X < 2X, which gives X > 1/3. This inequality hold true for all values 1/3 < X < 1/2. Hence TRUE
III. 1  x < x < 1/x Similar to equation II , 1  X < X gives X > 1/2 and X < 1/X gives X^2 1 < 0 (Cross multiplied since X is positive). X^21 < 0 can be written as (X1)(X+1) < 0.. This gives us than 1 < X < 1. Hence this inequality is true for all values of X between 1/2 to 1 exclusive. Hence TRUE
All three inequations hold, hence IMO its (E)




Re: If x is positive, which of the following may be true?
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07 Sep 2019, 06:13




