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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Absolute Vlaue Question

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members
Location: Utrecht, The Netherlands
Thanked: 318 times

by neelgandham » Thu Dec 15, 2011 7:03 am
If |10y - 4| > 7 and y < 1, which of the following could be y?

A) -0.8
B) -0.1
C) 0.1
D) 0
E) 1

Option E) y = 1 can be eliminated because y < 1 is the condition it should satisfy.
Option D) y = 0 and C) y = 0. 1 can be eliminated because -7<10y - 4<7 in both the cases
Option B) y = -0.1, 10y - 4 = -1-4 = -5. Implies |10y - 4| = 5 < 7 no the answer
Option A) y = -0.8, Is Correct ! Oh ok let me check.|10y - 4| = |-8-4| = 12 > 7 Superb!
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 349
Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members
Location: Austin, TX
Thanked: 236 times
GMAT Score:770

by GmatMathPro » Thu Dec 15, 2011 7:16 am
Strongt wrote:If |10y - 4| > 7 and y < 1, which of the following could be y?

A) -0.8

B) -0.1

C) 0.1

D) 0

E) 1

Could someone explain why the answer is A and not B
What did you do to get B?

Plugging in values works well here, as neelgandham demonstrates. If you want an algebraic way to solve it, you can do the following:

If, |10y-4|>7 then either 10y-4>7 or 10y-4<-7 (do you see why?) Now, solve these two inequalities one at a time:

10y-4>7
10y>11
y>1.1

OR

10y-4<-7
10y<-3
y<-0.3

So the solution is y<-0.3 OR y>1.1; But the questions specifies that y<1, so we can ignore the second part. y=-0.8 is the only one that satisfies both statements. Hence, ans: A
Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Wed Jan 05, 2011 3:32 amFollowed by: 1 member

by Strongt » Thu Dec 15, 2011 7:20 am
GmatMathPro wrote:
Strongt wrote:If |10y - 4| > 7 and y < 1, which of the following could be y?

A) -0.8

B) -0.1

C) 0.1

D) 0

E) 1

Could someone explain why the answer is A and not B
What did you do to get B?

Plugging in values works well here, as neelgandham demonstrates. If you want an algebraic way to solve it, you can do the following:

If, |10y-4|>7 then either 10y-4>7 or 10y-4<-7 (do you see why?) Now, solve these two inequalities one at a time:

10y-4>7
10y>11
y>1.1

OR

10y-4<-7
10y<-3
y<-0.3

So the solution is y<-0.3 OR y>1.1; But the questions specifies that y<1, so we can ignore the second part. y=-0.8 is the only one that satisfies both statements. Hence, ans: A
I guess that's what I'm missing
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 349
Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members
Location: Austin, TX
Thanked: 236 times
GMAT Score:770

by GmatMathPro » Thu Dec 15, 2011 8:01 am
To simplify matters, let's look at what it would mean for |x|>7. This says that the absolute value of x is greater than 7. But what does this mean? Essentially it means that the size of x, regardless of the sign, is bigger than 7. Clearly numbers bigger than 7 satisfy this. But numbers less than -7 also satisfy it. For example, |-8|=8, which is bigger than 7. The following number line shows all of the numbers that satisfy this inequality:

Image.

As you can see, this includes all numbers such that x>7 OR x<-7. So if we encounter |x|>7, we can always rewrite it equivalently as x>7 OR x<-7.

When we get to a more complicated expression, such as |4y-10|>7, it will work the exact same way. We can break it down into two separate inequalities by thinking, "for this to be true, the expression inside will either have to be greater than 7, OR less than -7, which, mathematically is written as 4y-10>7 OR 4y-10<-7. Now that we've rewritten it without the absolute value bars, we can use a traditional algebraic approach to solve for the solution set.





Strongt wrote:
GmatMathPro wrote:
Strongt wrote:If |10y - 4| > 7 and y < 1, which of the following could be y?

A) -0.8

B) -0.1

C) 0.1

D) 0

E) 1

Could someone explain why the answer is A and not B
What did you do to get B?

Plugging in values works well here, as neelgandham demonstrates. If you want an algebraic way to solve it, you can do the following:

If, |10y-4|>7 then either 10y-4>7 or 10y-4<-7 (do you see why?) Now, solve these two inequalities one at a time:

10y-4>7
10y>11
y>1.1

OR

10y-4<-7
10y<-3
y<-0.3

So the solution is y<-0.3 OR y>1.1; But the questions specifies that y<1, so we can ignore the second part. y=-0.8 is the only one that satisfies both statements. Hence, ans: A
I guess that's what I'm missing
Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1