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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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tommannanchery wrote:
How many of the following equalities are possible for at least one value of X ?\(x^2\) > X > \(x^3\) \(x^2\) > \(x^3\) > X \(x^3\) > X > \(x^2\)
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)
\(x^2\) >
\(x^3\) >
X True 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 ?\(x^2\) > X > \(x^3\) \(x^2\) > \(x^3\) > X \(x^3\) > X > \(x^2\)
(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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Answer should be C. iii is incorrect because when x > x2, which is when 0Posted 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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tommannanchery wrote:
How many of the following equalities are possible for at least one value of X ?\(x^2\) > X > \(x^3\) \(x^2\) > \(x^3\) > X \(x^3\) > X > \(x^2\)
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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abhimahna wrote:
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X ?\(x^2\) > X > \(x^3\) \(x^2\) > \(x^3\) > X \(x^3\) > X > \(x^2\)
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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rohit8865 wrote:
abhimahna wrote:
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X ?\(x^2\) > X > \(x^3\) \(x^2\) > \(x^3\) > X \(x^3\) > X > \(x^2\)
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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VeritasPrepKarishma wrote:
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X ?\(x^2\) > X > \(x^3\) \(x^2\) > \(x^3\) > X \(x^3\) > X > \(x^2\)
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)
\(x^2\) >
\(x^3\) >
X True 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?
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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tommannanchery wrote:
How many of the following equalities are possible for at least one value of X ?\(x^2\) > X > \(x^3\) \(x^2\) > \(x^3\) > X \(x^3\) > X > \(x^2\)
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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Re: How many of the following inequalities are possible for at least one
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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 &nbs
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57% (01:00) correct 
