BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Which of the following inequalities

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
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

by GMATGuruNY » Wed Feb 14, 2018 3:32 am
lheiannie07 wrote:Which of the following inequalities is equivalent to -2 < x < 4 ?

(A) | x - 2 | < 4
(B) | x - 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above
|x-y| = the DISTANCE between x and y

The midpoint between -2 and 4 = the average of -2 and 4 = (-2+4)/2 = 1.
-2 < x < 4 implies that x can be any value between -2 (3 places to the LEFT of 1) and 4 (3 places to the RIGHT of 1).
In other words: the distance between x and 1 must be less than 3.
In math terms:
|x-1| < 3.

The correct answer is B.

Similar problems:
https://www.beatthegmat.com/inequalities-t299234.html
https://www.beatthegmat.com/absolute-val ... 74256.html
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
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 14, 2018 7:36 am
lheiannie07 wrote:Which of the following inequalities is equivalent to -2 < x < 4 ?

(A) | x - 2 | < 4
(B) | x - 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above
We know that, if |something| < b (when b is positive), then -b < something < b
For example, if |2x+1| < 5 , then -b < 2x+1 < 5

We're going to apply the above rule IN REVERSE

Given: -2 < x < 4
Subtract 1 from all parts: -3 < x-1 < 3
So: |x-1| < 3

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Feb 14, 2018 2:58 pm
Hi lheiannie07,

We're asked which of the following inequalities is equivalent to -2 < X < 4. This question can be solved with a bit of 'brute force' and TESTing VALUES.

To start, let's see what happens to each answer when X approaches its MAXIMUM value (re: X gets really close to 4).

Answer A): |X - 2| < 4
Here, as X gets close to 4, |X - 2| gets really close to 2.... but that's not 'close' to the '4' in this inequality. Eliminate Answer A.

Answer B: |X - 1| < 3
Here, as X gets close to 4, |X - 1| gets really close to 3.... which is a match for this inequality. Keep Answer B for now.

Answer C: |X + 1| < 3
Here, as X gets close to 4, |X + 1| gets really close to 5.... but that's greater than the '4' in this inequality. Eliminate Answer C.

Answer D: |X + 2| < 4
Here, as X gets close to 4, |X + 2| gets really close to 6.... but that's greater than the '4' in this inequality. Eliminate Answer D.

At this point, the Answer is either B or E. Let's check see what happens to Answer B as X approaches its MINIMUM value (re: X gets really close to -2).

Answer B: |X - 1| < 3
Here, as X gets close to -2, |X - 1| gets really close to 3.... which is a match for this inequality. Answer B matches the range given by the initial inequality, so it MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8083
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Thu Feb 15, 2018 10:35 am
lheiannie07 wrote:Which of the following inequalities is equivalent to -2 < x < 4 ?

(A) | x - 2 | < 4
(B) | x - 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above
We need to go through the inequalities in the answer choices by solving them without the absolute value sign. However, at first glance, we can eliminate choices A and D since there is no way we can still have the 4 on the right hand side of the final answer when we solve the inequality without the absolute value sign (for example, x - 2 < 4 will become x < 6). So let's look at choice B first:

|x - 1| < 3 means x - 1 < 3 or -(x - 1) < 3.

If x - 1 < 3, then x < 4.

If -(x - 1) < 3, then x - 1 > -3 or x > -2.

Therefore, we have -2 < x < 4.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1