Re: If x is positive, which of the following could be correct ordering of
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28 Nov 2021, 09:56
First note that we are asked "which of the following COULD be the correct ordering" not MUST be.
Basically we should determine relationship between x, 1x and x2 in three areas: 0<1<2<.
x>2
1<x<2
0<x<1
When x>2 --> x2 is the greatest and no option is offering this, so we know that x<2.
If 1<x<2 --> 2x is greatest then comes x2 and no option is offering this.
So, we are left with 0<x<1:
In this case x2 is least value, so we are left with:
I. x2<2x<1x --> can 2x<1x? Can 2x2−1x<0, the expression 2x2−1 can be negative or positive for 0<x<1. (You can check it either algebraically or by picking numbers)
II. x2<1x<2x --> can 1x<2x? The same here 2x2−1x>0, the expression 2x2−1 can be negative or positive for 0<x<1. (You can check it either algebraically or by picking numbers)
Answer: D.
Second condition: x2<1x<2x
The question is which of the following COULD be the correct ordering not MUST be.
Put 0.9 --> x2=0.81, 1x=1.11, 2x=1.8 --> 0.81<1.11<1.8. Hence this COULD be the correct ordering.