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Line segment of finite length..

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Line segment of finite length..

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Another of question in GMAT Prep,

Question: Which of the following inequalities has a solution set such that when graphed on the number line is a single line segment of finite length?
A. x^4 ≥ 1
B. x^3 ≤ 27
C. x^2 ≥ 16
D. 2≤mod x≤5
E. 2 ≤ 3x+4 ≤ 6


Answer : E

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Any square functions will have symmetry about the y-axis,
so positive "squares" will have 2 solution sets for x^2 > ...

A. x^4 ≥ 1 ELIMINATE (as x^4 = (x^2)^2)
C. x^2 ≥ 16 ELIMINATE

Also:
B. x^3 ≤ 27 is open ended (infinite) ELIMINATE

With a modulus, x could be positive or negative, hence 2 solution sets:
D. 2≤mod x≤5 ELIMINATE

This leaves us with:
E. 2 ≤ 3x+4 ≤ 6

which is simply a finite linear segment (which is easily noticeable even without all the elimination above!)

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