[GMAT math practice question]
Which of the following inequalities is equivalent to |2x-|x|| < 3?
A. 0 < x < 2
B. 0 < x < 3
C. -1 < x < 3
D. 0 < x < 1
E. -3 < x < 1
Which of the following inequalities is equivalent to
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Since x=0 satisfies the given inequality, the correct answer must include 0 within its range.Max@Math Revolution wrote:[GMAT math practice question]
Which of the following inequalities is equivalent to |2x-|x|| < 3?
A. 0 < x < 2
B. 0 < x < 3
C. -1 < x < 3
D. 0 < x < 1
E. -3 < x < 1
Eliminate A, B and D.
Since x=2 satisfies the given inequality, the correct answer must include 2 within its range.
Eliminate E.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
|2x-|x||<3
=> -3 < 2x - |x| < 3
Case 1: If x ≥ 0, then |x| = x, and so
-3 < 2x - |x| < 3
=> -3 < x < 3
=> 0 ≤ x < 3, since x ≥ 0.
Case 2: If x < 0, then |x| = - x, and so
-3 < 2x - |x| < 3
=> -3 < 3x < 3
=> - 1< x < 1
=> - 1< x < 0, since x < 0.
Thus, -1 < x < 3.
Therefore, the answer is C.
Answer: C
|2x-|x||<3
=> -3 < 2x - |x| < 3
Case 1: If x ≥ 0, then |x| = x, and so
-3 < 2x - |x| < 3
=> -3 < x < 3
=> 0 ≤ x < 3, since x ≥ 0.
Case 2: If x < 0, then |x| = - x, and so
-3 < 2x - |x| < 3
=> -3 < 3x < 3
=> - 1< x < 1
=> - 1< x < 0, since x < 0.
Thus, -1 < x < 3.
Therefore, the answer is C.
Answer: C
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The given inequality is one with an absolute value expression within another absolute value expression. In general, this type of inequality is difficult to solve. Therefore, instead of solving it algebraically, we will analyze each answer choice to determine the correct answer. Notice that the correct answer should have the two endpoints of the interval (for example, the endpoints of choice A are 0 and 2) that makes |2x-|x|| equal to 3, and thus every value in between the endpoints will make |2x-|x|| less than 3.Max@Math Revolution wrote:[GMAT math practice question]
Which of the following inequalities is equivalent to |2x-|x|| < 3?
A. 0 < x < 2
B. 0 < x < 3
C. -1 < x < 3
D. 0 < x < 1
E. -3 < x < 1
A. 0 < x < 2
x = 0: |2(0) - |0|| = 0 .....This is not 3.
Choice A can't be the right answer.
B. 0 < x < 3
Choice B can't be the right answer either since when x = 0, |2x-|x|| is not equal to 3.
C. -1 < x < 3
x = -1: |2(-1) - |-1|| = |-2 - 1| = |-3| = 3
x = 3: |2(3) - |3|| = |6 - 3| = |3| = 3
We see that both endpoints make |2x-|x|| equal to 3. Thus, every value between -1 and 3, i.e., -1 < x < 3, will make 2x-|x|| less than 3.
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews