PS

[lionheart]

Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length?

A) x^4 >=(greater than or equal to) 1
B) x^3 =< 27
C) x^2 >= 16
D) 2 =< abs(x) =< 5
E) 2 =< 3x + 4 =< 6

Answer is E, don`t understand why it cant be D

[Nagm]

I believe this is from GMATfocus.

Except E all the options give more than 1 line segment. Easy way is to solve for X and plot graph

[RonPurewal]

uh oh, gmat focus is currently a banned source.

to the original poster: could you please confirm the source of this problem? if the problem is indeed from gmat focus and not gmatprep, we'll have to take down this thread. PLEASE don't post from banned sources (the banned sources list is in the sticky at the top of this folder). thank you.

[viksnme]

Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length?

A) x^4 >=(greater than or equal to) 1
B) x^3 =< 27
C) x^2 >= 16
D) 2 =< abs(x) =< 5
E) 2 =< 3x + 4 =< 6

Answer is E, don`t understand why it cant be D

This question is a GMAT Prep question and has already been discussed in the following link:
http://www.manhattangmat.com/forums/whi ... -t793.html

But basically, options A, B and C are out as they are non-linear.

D gives us 2 sets of solution sets when x is either positive or negative. When you solve you will get the following:
-5<=x<=-2 and 2<=x<=5

E is reduced to the inequality, -2/3<=x<=2/3. This gives just 1 solution set and hence is the correct answer.

Note that inequalities always gives us an area when plotted on a graph. I had trouble understanding how an area can be compared with a single line segment of finite length, as was being asked in the question, until I focussed on the part of the question that says 'when graphed on the number line'. GMAT has very cleverly put this in order to confuse anyone who can fall into this trap. So basically, when the solution set is plotted on the number line, it is reduced to a line segment which would be of finite length for linear inequalities.

[RonPurewal]

I had trouble understanding how an area can be compared with a single line segment of finite length, as was being asked in the question, until I focussed on the part of the question that says 'when graphed on the number line'. GMAT has very cleverly put this in order to confuse anyone who can fall into this trap. So basically, when the solution set is plotted on the number line, it is reduced to a line segment which would be of finite length for linear inequalities.

on problems like this, the number line should be your default! you shouldn't have to be told to use a number line on this sort of problem.

in particular:
if you have a problem with ONE VARIABLE, then you should graph the solution(s) on a NUMBER LINE - because the number line is the device that's specifically crafted to show numbers/intervals for one variable only.

if you have a problem with TWO VARIABLES, then you should graph the solution(s) on a COORDINATE PLANE - because the purpose of the coordinate plane is to show relationships between two variables.

these are defaults; if you only have one variable, there is no reason whatsoever to use a coordinate plane at all, much less by default.

[viksnme]

I had trouble understanding how an area can be compared with a single line segment of finite length, as was being asked in the question, until I focussed on the part of the question that says 'when graphed on the number line'. GMAT has very cleverly put this in order to confuse anyone who can fall into this trap. So basically, when the solution set is plotted on the number line, it is reduced to a line segment which would be of finite length for linear inequalities.

on problems like this, the number line should be your default! you shouldn't have to be told to use a number line on this sort of problem.

in particular:
if you have a problem with ONE VARIABLE, then you should graph the solution(s) on a NUMBER LINE - because the number line is the device that's specifically crafted to show numbers/intervals for one variable only.

if you have a problem with TWO VARIABLES, then you should graph the solution(s) on a COORDINATE PLANE - because the purpose of the coordinate plane is to show relationships between two variables.

these are defaults; if you only have one variable, there is no reason whatsoever to use a coordinate plane at all, much less by default.

Ron, many thanks for pointing this out. I did get mixed up with inequalities with one and with two variables. I understand it better now.