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
Line segment of finite length..
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
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!)
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!)