Last visit was: 14 Jul 2024, 08:04 It is currently 14 Jul 2024, 08:04
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Is it true that |b - 2| + |b + 8| = 10 ?

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 04 May 2007
Posts: 71
Own Kudos [?]: 25 [8]
Given Kudos: 0
Current Student
Joined: 28 Dec 2004
Posts: 1578
Own Kudos [?]: 645 [0]
Given Kudos: 2
Location: New York City
Concentration: Social Enterprise
Schools:Wharton'11 HBS'12
Senior Manager
Joined: 26 Jul 2007
Posts: 359
Own Kudos [?]: 368 [0]
Given Kudos: 0
Concentration: Real Estate Development
Schools:Stern, McCombs, Marshall, Wharton
Q42  V35
Director
Joined: 10 Jun 2007
Posts: 649
Own Kudos [?]: 1600 [0]
Given Kudos: 0
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
gmatiscoming wrote:
Is it true that ? |b-2|+|b+8|=10

(1) b less than or equal to 2
(2) b is greater than or equal to negative 8

C.

These type of questions, it is much faster if you realize the critical points of the equation. In this case, critical points are b=2 and b=-8.
From this, you know that there are three intervals that the equation must satisfy.

A interval: b<-8
B interval: -8<b<2
C interval: b>2

If you find that b fall into one of these interval, then it must be right. (1) doesn't since it falls into intervals A and B, so INSUFFICIENT. (2) doesn't either because it falls into interval B and C, INSUFFICIENT. Together, it falls into interval B. SUFFICIENT.
Intern
Joined: 18 Jun 2007
Posts: 47
Own Kudos [?]: 9 [0]
Given Kudos: 0
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
I am not sure how C could be correct..

There are only 2 possible values of B that could satisfy the equation

|b-2|+|b+8|=10 , B is either2 or -8

Combining C

b<2>=-8

Combining both

B could have a value between -8......2 ?

Why are we not considering the values between ?
Thanks for clarrifying..
Director
Joined: 10 Jun 2007
Posts: 649
Own Kudos [?]: 1600 [0]
Given Kudos: 0
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
|b-2|+|b+8|=10

Plug in any number between -8 and 2 will satisfy the equation.
Director
Joined: 10 Jun 2007
Posts: 649
Own Kudos [?]: 1600 [0]
Given Kudos: 0
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
gmatiscoming wrote:
Is it true that ? |b-2|+|b+8|=10

(1) b less than or equal to 2
(2) b is greater than or equal to negative 8

C.

These type of questions, it is much faster if you realize the critical points of the equation. In this case, critical points are b=2 and b=-8.
From this, you know that there are three intervals that the equation must satisfy.

A interval: b<-8
B interval: -8<b<2
C interval: b>2

If you find that b fall into one of these interval, then it must be right. (1) doesn't since it falls into intervals A and B, so INSUFFICIENT. (2) doesn't either because it falls into interval B and C, INSUFFICIENT. Together, it falls into interval B. SUFFICIENT.

*Additional comment: for this method to be useful, you should at least plug in a value from those interval to see if which one equals 10.
VP
Joined: 01 May 2006
Posts: 1032
Own Kudos [?]: 252 [0]
Given Kudos: 0
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
(C) for me too

|b-2|+|b+8|=10

I suggest to analyse quickly what is going on by replacing the absolutes.

o If b < -8 then
|b-2|+|b+8|
= -(b-2) - (b+8)
= -2*b - 6 >>> Not 10 and could not be

o If -8 =< b =< 2 then
|b-2|+|b+8|
= -(b-2) + (b+8)
= 10 >>> Sounds good

o If b > 2 then
|b-2|+|b+8|
= +(b-2) + (b+8)
= 2*b + 6 >>> Not 10 and could not be

From 1
b <= 2 >>>> So, we cannot conclude as it could be that -8 =< b =< 2 or b < -8

INSUFF.

From 2
b >= -8 >>>> So, we cannot conclude again as it could be that -8 =< b =< 2 or b > 2.

INSUFF.

Both (1) & (2)
Bongo.... It's -8 =< b =< 2 and we have seen that |b-2|+|b+8| = 10.

SUFF.
Current Student
Joined: 28 Dec 2004
Posts: 1578
Own Kudos [?]: 645 [0]
Given Kudos: 2
Location: New York City
Concentration: Social Enterprise
Schools:Wharton'11 HBS'12
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
If I can only freakin add on D day..arrrgggggggh...

guys any suggestions on how to avoid such mistakes????
Director
Joined: 10 Jun 2007
Posts: 649
Own Kudos [?]: 1600 [0]
Given Kudos: 0
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
fresinha12 wrote:
If I can only freakin add on D day..arrrgggggggh...

guys any suggestions on how to avoid such mistakes????

It happens to me too when I try to do it too fast or do it at work. I suggest writing it out step by step or get a good sleep. Or maybe it is just rainy today :D
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5275
Own Kudos [?]: 4178 [1]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
1
Kudos
gmatiscoming wrote:
Is it true that |b - 2| + |b + 8| = 10 ?

(1) b less than or equal to 2
(2) b is greater than or equal to negative 8

Asked: Is it true that |b - 2| + |b + 8| = 10 ?
-8---------b------------2
For $$-8 \leq b \leq 2$$
|b-2|+|b+8| = 10

(1) b less than or equal to 2
If b is greater than or equal to -8
|b-2|+|b+8| = 10
Otherwise NOT
NOT SUFFICIENT

(2) b is greater than or equal to negative 8
If b less than or equal to 2
|b-2|+|b+8| = 10
Otherwise NOT
NOT SUFFICIENT

(1) + (2)
(1) b less than or equal to 2
(2) b is greater than or equal to negative 8
For $$-8 \leq b \leq 2$$
|b-2|+|b+8| = 10
SUFFICIENT

IMO C
VP
Joined: 18 Dec 2017
Posts: 1161
Own Kudos [?]: 1046 [0]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
gmatiscoming wrote:
Is it true that |b - 2| + |b + 8| = 10 ?

(1) b less than or equal to 2
(2) b is greater than or equal to negative 8

When you read statement 1, it seems sufficient. Fair enough.

When you read statement 2, you might want to check for b=-9.
$$11+1=12$$ which is not equal to 10. That means we need statement 2 as well.

Hence C

Thank you!
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4918
Own Kudos [?]: 7799 [0]
Given Kudos: 220
Location: India
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
Hi,

When solving for questions where you have two absolute values added to each other, the best way is to work with distances traveled on the number line.

The absolute value is defined as the distance traveled from the origin on the number line, so if |x - 2| = 5, this means that the distance traveled from the origin i.e. 2 has to be 5 units. Imagine a person standing at 2 on the number line and having to travel a distance of 5 units from 2. The person can move left to a distance of 5 units and will end up at -3 or he can move right to a distance of 5 units and will end up at 7. These would be the solutions to the equation |x - 2| = 5.

Now let us use this basic understanding to solve the question given.

|b - 2| + |b + 8| = 10

The question says that the total distance traveled from 2 to -8 is 10 units. So if we imagine two people, one who is at 2 and the other who is at -8 the total distance that needs to be covered by both together is 10 units. So the only way this can be done is if both of them meet art any point in between 2 and -8.

So the question just asks us if b is between -8 and 2.

Attachment:

Capture.PNG [ 93.31 KiB | Viewed 6448 times ]

Statement 1 and Statement 2 together give us this.

Non-Human User
Joined: 09 Sep 2013
Posts: 33968
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Is it true that |b - 2| + |b + 8| = 10 ? [#permalink]
Moderator:
Math Expert
94342 posts