GMAT PREP inequalities

Remember that you are plotting values for X such that the expression holds true.

Answer D will have a number line with two segments: One between -2 and -5 and a second between 2 and 5.

It IS finite, but isn't one segment.

Haha, I tried making a graph, but the spacing wouldn't work.

Can anyone pls let me know how the option-1 to 4 represent a line segment of fixed length? I am not getting the approach ...

camitava wrote:Can anyone pls let me know how the option-1 to 4 represent a line segment of fixed length? I am not getting the approach ...

The problem is that most of them do NOT represent a line segment of finite length.

(1) x^4 >= 1 is true for all x < -1 and all x > 1: two infinite lines.

(2) x^3 <= 27 is true for all x <= 3: an infinite line.

(3) x^2 >= 16 is true for all x >= 4 and all x <= -4: two infinite lines.

(4) 2 <= |x| <= 5 is true for -5 <=x <= -2 AND 2 <= x <= 5: TWO finite line segments.

However:

(5) 2 <= 3x + 4 <= 6 is true for -(2/3) <= x <= 2/3: a finite line segment.

Stuart Kovinsky wrote:

camitava wrote:Can anyone pls let me know how the option-1 to 4 represent a line segment of fixed length? I am not getting the approach ...

The problem is that most of them do NOT represent a line segment of finite length.

(1) x^4 >= 1 is true for all x < -1 and all x > 1: two infinite lines.

(2) x^3 <= 27 is true for all x <= 3: an infinite line.

(3) x^2 >= 16 is true for all x >= 4 and all x <= -4: two infinite lines.

(4) 2 <= |x| <= 5 is true for -5 <=x <= -2 AND 2 <= x <= 5: TWO finite line segments.

However:

(5) 2 <= 3x + 4 <= 6 is true for -(2/3) <= x <= 2/3: a finite line segment.

Hi Stuart,

I did not understand this. I marked D as an option reasoning because x is between 2 and 5. i understand |x| can have + or - values, but x has to be between or equat to 2 and 5 and hence this has a finite line. Pls. help me understand.

Thanks,

|X| is where X could be negative value or a positive value.

pre-gmat wrote:|X| is where X could be negative value or a positive value.

If x is negative then x cannot be between 2 and 5 and hence i mentioned my question still remains same as how come option D represent 2 finitie lines.

You need to solve the inequality 2<=|x|

If X is positive, then 2<=x

If x is negative then X<=-2

Similarly

|x|<=5

if x is positive then X<=5
If x is negative then X>=-5

so as Stuart points out correctly there are two line segments:
-5 <=x <= -2 AND 2 <= x <= 5

pre-gmat wrote:You need to solve the inequality 2<=|x|

If X is positive, then 2<=x

If x is negative then X<=-2

Similarly

|x|<=5

if x is positive then X<=5
If x is negative then X>=-5

so as Stuart points out correctly there are two line segments:
-5 <=x <= -2 AND 2 <= x <= 5

ah... now i got what you are saying...
the above equations can also be written as
If x is negative then X<=-2 OR -x>=2
If x is negative then X>=-5 OR -x<=5
I did visualize the first part but didn't notice the OR part where -x can also fall between 2 and 5 since x is negative and for a negative value the inqualities behave differently.

Thanks all!