GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Sep 2018, 18:05

### 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
Your Progress

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

# Which of the following is the sum of solutions of |x+1| = 2|x-1|?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Nov 2017
Posts: 28
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
Which of the following is the sum of solutions of |x+1| = 2|x-1|?  [#permalink]

### Show Tags

10 Jul 2018, 04:15
2
1
15
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:39) correct 41% (01:51) wrong based on 231 sessions

### HideShow timer Statistics

Which of the following is the sum of solutions of |x+1| = 2|x-1|?

A. 4
B. 6
C. 8
D. $$\frac{20}{3}$$
E. $$\frac{10}{3}$$
Math Expert
Joined: 02 Sep 2009
Posts: 49496
Re: Which of the following is the sum of solutions of |x+1| = 2|x-1|?  [#permalink]

### Show Tags

10 Jul 2018, 04:33
2
1
Karthik200 wrote:
Which of the following is the sum of solutions of |x+1| = 2|x-1|?

A. 4
B. 6
C. 8
D. $$\frac{20}{3}$$
E. $$\frac{10}{3}$$

Square the given equation:

$$(x + 1)^2 = 4(x - 1)^2$$;

$$4(x - 1)^2 - (x + 1)^2 = 0$$;

Apply a^2 - b^2 = (a - b)(a + b) to the above: $$(2(x - 1) - (x + 1))(2(x - 1) + (x + 1)) = 0$$;

$$(x - 3)(3x - 1) = 0$$;

$$x = 3$$ or $$x= \frac{1}{3}$$.

The sum of the roots $$= 3 + \frac{1}{3} = \frac{10}{3}$$.

Answer: E.

OR: |x+1| = 2|x-1| can be expanded either the way that both LHS and RHS have the same sign or different signs. So

Either: x + 1 = 2(x - 1) --> x = 3.
Or: x + 1 = -2(x - 1) --> x = 1/3.

The sum of the roots $$= 3 + \frac{1}{3} = \frac{10}{3}$$.

Answer: E.
_________________
Intern
Joined: 08 Jul 2018
Posts: 39
Re: Which of the following is the sum of solutions of |x+1| = 2|x-1|?  [#permalink]

### Show Tags

11 Jul 2018, 22:36
Karthik200 wrote:
Which of the following is the sum of solutions of |x+1| = 2|x-1|?

A. 4
B. 6
C. 8
D. $$\frac{20}{3}$$
E. $$\frac{10}{3}$$

Hi,

Squaring both sides will do the trick.
I started plugging in values into $$|x+1| / /|x-1|=2$$ and eliminating options , took 2+ mins.
_________________

“Pain + Reflection = Progress”
― Ray Dalio

Senior Manager
Joined: 12 Feb 2015
Posts: 436
Which of the following is the sum of solutions of |x+1| = 2|x-1|?  [#permalink]

### Show Tags

16 Jul 2018, 09:51
1
1
Scenerio 1: x + 1 = 2(x - 1) Implies that x = 3.
Scenerio 2: (x + 1) = -2(x - 1) Implies that x = 1/3. [The reason we cannot use a negative sign on both the sides when we are equating in scenerio 2 is then there will not be any difference between scenario 1 and 2]

Sum of possible solutions is $$\frac{10}{3}$$

Option E is the correct answer
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

Senior Manager
Joined: 14 Dec 2017
Posts: 479
Re: Which of the following is the sum of solutions of |x+1| = 2|x-1|?  [#permalink]

### Show Tags

16 Jul 2018, 10:26
Karthik200 wrote:
Which of the following is the sum of solutions of |x+1| = 2|x-1|?

A. 4
B. 6
C. 8
D. $$\frac{20}{3}$$
E. $$\frac{10}{3}$$

Given: |x+1| = 2|x-1|

For x+1 > 0 & x-1 > 0, we have x>-1 & x>1, we get x+1 = 2(x-1), hence x = 3 > -1, is within range.

For x+1 < 0 & x-1 < 0, we have x<-1 & x<1, we get -(x+1) = -2(x-1), hence x = 3 > 1, is not acceptable

For x+1 > 0 & x-1 < 0, we have x>-1 & x<1, we get x+1 = -2(x-1), hence x = 1/3 < 1 & > -1, is within range.

For x+1 < 0 & x-1 > 0, we have x<-1 & x>1, we get -(x+1) = 2(x-1), hence x = 1/3 < 1, is not acceptable.

Hence, we have, x = 3 & 1/3

Sum of solutions = 3 + 1/3 = 10/3

Answer E.

Thanks,
GyM
_________________
Manager
Joined: 07 Feb 2017
Posts: 180
Re: Which of the following is the sum of solutions of |x+1| = 2|x-1|?  [#permalink]

### Show Tags

18 Jul 2018, 20:03
x+1=2x-2
x=3

-x-1=2x-2
x=1/3

Answer E. 10/3

THIS PROBLEM IS EASY
Re: Which of the following is the sum of solutions of |x+1| = 2|x-1|? &nbs [#permalink] 18 Jul 2018, 20:03
Display posts from previous: Sort by

# Which of the following is the sum of solutions of |x+1| = 2|x-1|?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.