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How many of the following inequalities are possible for at least one
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How many of the following inequalities are possible for at least one value of x? I. \(x^2 > x > x^3\) II. \(x^2 > x^3 > x\) III. \(x^3 > x > x^2\) A. I only B. II only C. I and II only D. I, II, and III only E. none
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Originally posted by tommannanchery on 31 Jul 2016, 12:21.
Last edited by Bunuel on 03 Jul 2017, 03:23, edited 2 times in total.
Renamed the topic and edited the question.




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Re: How many of the following inequalities are possible for at least one
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31 Jul 2016, 22:37
tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none The question is based on your understanding of how x, x^2 and x^3 behave in different regions of the number line. x^2 > x for all negative x and when x > 1 x^3 > x for x > 1 and 1 < x < 0. (i) \(x^2\) > X > \(x^3\)True for all negative x. (ii) \(x^2\) > \(x^3\) > XTrue for 1 < x< 0 (iii) \(x^3\) > X > \(x^2\)x is greater than x^2 between 0 and 1 only. But in that region x^3 is not greater than x. So this will not hold. Answer (C)
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Re: How many of the following inequalities are possible for at least one
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tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none (1) Let X=2 then we get a yes answer (2) Let X=0.5 then we get a yes (3) none of X satisfies Ans C
Originally posted by rohit8865 on 31 Jul 2016, 19:15.
Last edited by rohit8865 on 01 Aug 2016, 07:31, edited 2 times in total.



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Re: How many of the following inequalities are possible for at least one
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01 Aug 2016, 01:26
Answer should be C. iii is incorrect because when x > x2, which is when 0 Posted from my mobile device



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Re: How many of the following inequalities are possible for at least one
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01 Aug 2016, 08:30
tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none Answer is D. For (i)  Consider x=1/3. => We can have X= 2/27 which is between 1/9 and 1/27 For (ii) Consider x= 1/2= > We can have X=0 which is less than 1/4 and 1/8. For (iii)  Consider x= 2 => We can have X = 5 which is between 8 and 4. Hence, we can have each of the above statements valid for different vales of x and X. NOTE : I have solved the above question based on the assumption that x and X are two different variables.
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Re: How many of the following inequalities are possible for at least one
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01 Aug 2016, 09:29
abhimahna wrote: tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none Answer is D. For (i)  Consider x=1/3. => We can have X= 2/27 which is between 1/9 and 1/27 For (ii) Consider x= 1/2= > We can have X=0 which is less than 1/4 and 1/8. For (iii)  Consider x= 2 => We can have X = 5 which is between 8 and 4. Hence, we can have each of the above statements valid for different vales of x and X. NOTE : I have solved the above question based on the assumption that x and X are two different variables.if the highlighted part is correct then there is no need of any option there always exist a number in between Karishma Please give your 2 cents also because source mentioned is veritas...



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Re: How many of the following inequalities are possible for at least one
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01 Aug 2016, 09:45
rohit8865 wrote: abhimahna wrote: tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none Answer is D. For (i)  Consider x=1/3. => We can have X= 2/27 which is between 1/9 and 1/27 For (ii) Consider x= 1/2= > We can have X=0 which is less than 1/4 and 1/8. For (iii)  Consider x= 2 => We can have X = 5 which is between 8 and 4. Hence, we can have each of the above statements valid for different vales of x and X. NOTE : I have solved the above question based on the assumption that x and X are two different variables.if the highlighted part is correct then there is no need of any option there always exist a number in between Karishma Please give your 2 cents also because source mentioned is veritas... Correct bro. I agree to what you said. Can anyone please help here?
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Re: How many of the following inequalities are possible for at least one
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26 Mar 2017, 22:11
VeritasPrepKarishma wrote: tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none The question is based on your understanding of how x, x^2 and x^3 behave in different regions of the number line. x^2 > x for all negative x and when x > 1 x^3 > x for x > 1 and 1 < x < 0. (i) \(x^2\) > X > \(x^3\)True for all negative x. (ii) \(x^2\) > \(x^3\) > XTrue for 1 < x< 0 (iii) \(x^3\) > X > \(x^2\)x is greater than x^2 between 0 and 1 only. But in that region x^3 is not greater than x. So this will not hold. Answer (C) Responding to a pm: Quote: I have a doubt for the second one?
0.5 (1/2) lies in the range 1<x<0
so if we consider x=1/2; then x2 = 1/4 and x3 = 1/8
in this case x3>x2>x _. so second case does not hold
Note that square of a real number is never negative. If \(x = 1/2,\) \(x^2 = (1/2)^2 = (1/2)*(1/2) = 1/4\) \(x^3 = (1/2)*(1/2)*(1/2) = 1/8\) So \(x^2 > x^3 > x\)
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Re: How many of the following inequalities are possible for at least one
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03 Jul 2017, 03:16
tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none Bunuel: Can you please check this question? I did not find any values for which (iii) holds. Shouldn't OA be C?



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Re: How many of the following inequalities are possible for at least one
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03 Jul 2017, 03:24
warriorguy wrote: tommannanchery wrote: How many of the following equalities are possible for at least one value of X?
(i) \(x^2\) > X > \(x^3\) (ii) \(x^2\) > \(x^3\) > X (iii) \(x^3\) > X > \(x^2\)
A. i only B. ii only C. i and ii only D. i, ii, and iii only E. none Bunuel: Can you please check this question? I did not find any values for which (iii) holds. Shouldn't OA be C? Yes. The correct answer is C, not D. Edited. Thank you.
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Re: How many of the following inequalities are possible for at least one
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02 Oct 2018, 01:44
saichandm wrote: Answer should be C. iii is incorrect because when x > x2, which is when 0<x<1), x3 is less than x2!!
Posted from my mobile device For a problem that hinges on a conceptual understanding of properties of numbers with exponents, plugging in is a natural first approach. So try values in meaningfully different ranges. Say x is 2: that makes \(x^2\)=4 and \(x^3\)=8 \(So, x^3 > x^2 > x\) which doesn't work for any of the inequalities. Now say x is 2: that makes \(x^2\) \(x^3\)=8 \(So, x^2 > x > x^3\) Having tried both negative and positive integers, consider what other ranges are left: fractions between 0 and 1 and fractions between 0 and 1. Inequality (ii) will be true for any fraction between 0 and 1, so it's possible, but inequality (iii) never works: the only numbers for which x > \(x^2\) are fractions between 0 and 1, but for all such numbers \(x^2\) is also greater than \(x^3\) Answer C
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Re: How many of the following inequalities are possible for at least one
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