Which of the following can never be true?

Question

A.  x^3 < x < x^2 < x^4

B.  \frac{1}{x} < x < \frac{1}{x^2} < \frac{1}{x^3}

C.  x < \frac{1}{x} < x^2 < x^4

D.  x < \frac{1}{x} < x^2

E.  \frac{1}{x} < x < x^4 < x^2

Bunuel · Answer

EXPERT'S GLOBAL OFFICIAL VIDEO EXPLANATION

https://www.youtube.com/watch?v=59mwllTFZzs

Ckey15 · Answer

Hello, 
can you give an example of E? I can't seem to find a value of x that satisfies it

Bunuel · Answer

The inequality 1/x < x < x^4 < x^2 implies -1 < x < 0, so any negative number between -1 and 0 will satisfy it. For example, x = -0.5 works.

Rishiman · Answer

Since there is no detailed explain action on this question, I’m sharing one which helped me.

For these kind of questions, one needs to check for all 4 possible ranges - x>1, 0<x<1, -<x<0, x<0

Some basic relationship in the number line questions are -

For x>1 ——-> X4>x3>x2>x
For 0<x<1 ——> x>x2>x3>x4
For -1<x<0 ——-> x2>x4>x>x3
For x<-1 ——> x4>x2>x>x3

Now, let us look at choice ->

E- x2>x4 - that is possible in the range - -1<x<0, now, all we have to check that in this range is 1/x<x. Yes it is.
D - Visualise this, between x an x2 there there is 1/x, now we know x2>x for x>1 and x<-1, all we have to check if 1/x>x, that is possible only in the negative range.
C - In this one x4>x2, which is possible in x>1 range and x<-1 range, again the same relationship is followed between x, 1/x ad x2 (as we saw in C), hence range is x<-1.
A - x4>x2 inn x>1 and x<-1 but x>x3 is only possible in x<-1. Hence, that is range.
B - Although, 1/x<x is only possible in x>1 range, but the relationship between 1/x3<1/x2 doesn’t hold in that range. Hence,The answer is B.

Which of the following can never be true?

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Which of the following can never be true?

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