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# Find the median of the following numbers:

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Intern
Joined: 21 Oct 2017
Posts: 14
Find the median of the following numbers:  [#permalink]

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16 Mar 2019, 20:25
4
00:00

Difficulty:

75% (hard)

Question Stats:

45% (02:07) correct 55% (02:15) wrong based on 20 sessions

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Find the median of the following numbers:

-$$(\frac{1}{2})^{(\frac{-1}{3})}$$ ; -$$(\frac{1}{4})^{(\frac{-1}{3})}$$ ; -$$(\frac{1}{4})^{(\frac{-1}{2})}$$ ; -$$(\frac{1}{4})^{(\frac{-2}{3})}$$ ; -$$(\frac{1}{3})^{(\frac{-1}{2})}$$

A. -$$(\frac{1}{2})^{(\frac{-1}{3})}$$

B. -$$(\frac{1}{4})^{(\frac{-1}{3})}$$

C. -$$(\frac{1}{4})^{(\frac{-1}{2})}$$

D. -$$(\frac{1}{4})^{(\frac{-2}{3})}$$

E. -$$(\frac{1}{3})^{(\frac{-1}{2})}$$
Senior Manager
Joined: 20 Mar 2018
Posts: 412
Location: Ghana
Concentration: Finance, Real Estate
Find the median of the following numbers:  [#permalink]

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18 Mar 2019, 11:10
(1/2)^(-1/3)= (1/0.5^(1/3)) =cuberoot(1/0.5) =cuberoot(2)~1.25

(1/4)^(-1/3)= (1/0.25^(1/3))=cube root(4)~1.60
(1/4)^(-1/2)=(1/0.25^(1/2)=root(4)=2,

(1/4)^(-2/3)=(1/0.25^(2/3))=cube root (16)~2.5

(1/3)^(-1/2)=(1/0.33^(1/2))=root(3.03)~1.74
now we arrange them since they are 5 we know the median will be the 3rd term. Now we have 1.25,1.60,*1.74*,2,2.5 so median is (1/4)^(-2/3)
Ans is E
Hope it helps

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Intern
Joined: 20 Jul 2018
Posts: 13
Re: Find the median of the following numbers:  [#permalink]

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18 Mar 2019, 12:36
1
Let's do analysis of the question this question is checking three aspects of maths - Exponents, Statistics and PEMDAS Rules.

1) Exponents - if fraction is raised to the -ve power convert that fraction into reciprocal and then make exponent positive (BCZ exponents are always positive)

2) Statistics - Median def

3) PEMDAS - first off all raise the power or take root of the number then apply the -ve sign.

1) -(1/2)^(-1/3) = - {(2)^1/3}~ -1.25
2)-(1/4)^(-1/3)= -{(4)^1/3} ~-1.5
3)-(1/4)^(-1/2)= - {(4)^1/2}~-2
4)-(1/4)^(-2/3)= -{(4)^2/3} ~ -2.49
5) -(1/3)^(-1/2) =- {(3)^1/2} ~ -1.73

arrange the above terms in ascending way: -2.49 , -2 , -1.73, -1.58 , -1.25

the middle term is -1.73 hence the option is E .(IMO)
Re: Find the median of the following numbers:   [#permalink] 18 Mar 2019, 12:36
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