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.
GMAT PREP inequalities
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
The problem is that most of them do NOT represent a line segment of finite length.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 ...
(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 | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
-
anju
- Master | Next Rank: 500 Posts
- Posts: 258
- Joined: Thu Mar 29, 2007 3:15 am
- Thanked: 7 times
- Followed by:1 members
Hi Stuart,Stuart Kovinsky wrote:The problem is that most of them do NOT represent a line segment of finite length.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 ...
(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.
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,
-
anju
- Master | Next Rank: 500 Posts
- Posts: 258
- Joined: Thu Mar 29, 2007 3:15 am
- Thanked: 7 times
- Followed by:1 members
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.pre-gmat wrote:|X| is where X could be negative value or a positive value.
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
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
-
anju
- Master | Next Rank: 500 Posts
- Posts: 258
- Joined: Thu Mar 29, 2007 3:15 am
- Thanked: 7 times
- Followed by:1 members
ah... now i got what you are saying...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
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!
