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

Redeem

Inequality

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sun Jul 31, 2011 10:55 am
Followed by:1 members

Inequality

by HeyArnold » Wed Aug 03, 2011 5:47 pm
Which of the following inequalities is equivalent to the shaded part of the number line shown to the right?

(The number line is x is between -7 and -1 inclusive)

A) |x| > or = -7
B) |x-4| > or = 3
C) |x+4| < or = 3
D) |x| < or = -1
E) |x+3| < or = 4

[spoiler]OA C.... Why is E wrong?! Every point seems to satisfy E as well![/spoiler]
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 401
Joined: Tue May 24, 2011 1:14 am
Thanked: 37 times
Followed by:5 members

by MBA.Aspirant » Wed Aug 03, 2011 6:04 pm
HeyArnold wrote:Which of the following inequalities is equivalent to the shaded part of the number line shown to the right?

(The number line is x is between -7 and -1 inclusive)

A) |x| > or = -7
B) |x-4| > or = 3
C) |x+4| < or = 3
D) |x| < or = -1
E) |x+3| < or = 4

[spoiler]OA C.... Why is E wrong?! Every point seems to satisfy E as well![/spoiler]
-7 ≤ x ≤ -1 this is what we're looking for


A) |x| ≥ -7

-7 ≤ x ≤ 7


B) |x-4| ≥ 3

x-4 ≥ 3, x ≥ 7


C) |x+4| ≤ 3

x+4 ≤ 3, x ≤ -1

x+4 ≥ -3, x ≥ -7

-7 ≤ x ≤ -1
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 Aug 03, 2011 6:14 pm
HeyArnold wrote:Which of the following inequalities is equivalent to the shaded part of the number line shown to the right?

(The number line is x is between -7 and -1 inclusive)

A) |x| > or = -7
B) |x-4| > or = 3
C) |x+4| < or = 3
D) |x| < or = -1
E) |x+3| < or = 4

[spoiler]OA C.... Why is E wrong?! Every point seems to satisfy E as well![/spoiler]
To answer your question about answer choice E, we can plug in some values to see that x=0 is a solution to |x+3| < 4 , but 0 does not fall between -7 and -1 (inclusive) on the number line.

Alternatively, if |x+3| < 4, then -4 < x+3 < 4
Subtract 3 from both sides to get -7 < x < 1

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pm
Location: New York City
Thanked: 130 times
Followed by:33 members
GMAT Score:780

by gmatboost » Wed Aug 03, 2011 10:09 pm
Some general rules for Absolute Value Inequalities that you should remember:

If the solution is bounded on both sides, like a < x < b, then the answer will look like |?| < number (LESS THAN)

If the solution has two regions, like x < a OR x > b, then the answer will look like |?| > number (GREATER THAN)

Either way, there are two boundary points, a and b. Find their average (aka the number half-way between them). Call this V.
Now, find the distance from either a or b to V. Call this D.

The answer is always |x - V| (LESS THAN OR GREATER THAN) D.

I know this is a lot of words, but applying it doesn't take too long:
Bounded solution means |?| < number
The number half-way between -1 and -7 is -4. The distance from either one to -4 is 3.
|x - V| (LESS THAN OR GREATER THAN) D becomes
|x - -4| < 3 or |x + 4| < 3

Yes, you can plug in, but on the test, chances are good that you are going to have to plug in 3-4 times on this type of question to narrow it down to just one answer. And, as you saw, it's not always obvious WHAT to plug in on this type of question to distinguish between two similar choices.

This is (in my opinion) one case where using the algebra can save you time.
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.
Top
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Tue Jul 05, 2011 1:13 am

by StoneBlack » Wed Aug 03, 2011 10:26 pm
In case of E,
Simply solve for x for both positive and negative of the absolute terms.

|x+3|<=4

for x+3>0,

x+3<=4
=> x<=1 (subtracting 3 from both sides) .......(1)

for x+3<0,
-(x+3)<=4
=> -x-3<=4
=> -x<=7 (Adding 3 on both sides)
=> x>=-7 (Negating both sides and changing sign hence).......(2)

Combining (1) and (2),

-7=<x<=1.

Hence it does not come within -7<=x<=-1 as asked in the question.
Top
Post new topic Post Reply
• Page 1 of 1