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

 It is currently 18 Apr 2019, 21:35

### 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

# What is the value of x?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 416
What is the value of x?  [#permalink]

### Show Tags

25 Jun 2014, 09:26
3
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:25) correct 33% (01:28) wrong based on 188 sessions

### HideShow timer Statistics

What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1
Math Expert
Joined: 02 Sep 2009
Posts: 54371
What is the value of x?  [#permalink]

### Show Tags

25 Jun 2014, 09:30
2
What is the value of x?

(1) $$|x+5| = |x+3|$$ --> square both sides: $$(x+5)^2=(x+3)^2$$ --> $$x^2+10 x+25 = x^2+6 x+9$$ --> $$4x=-16$$ --> $$x=-4$$. Sufficient.

(2) $$|x+3| = 1$$ --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.

_________________
Senior Manager
Joined: 13 Jun 2013
Posts: 274
Re: What is the value of x?  [#permalink]

### Show Tags

25 Jun 2014, 13:00
2
goodyear2013 wrote:
What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1

we can also use the number line to calculate the value of x

st.1 for x<-5, and x>-3 we have now possible solution.
but for -5<x<-3, we have
|x+5|=x+5 and |x+3|= -x-3

thus we have x+5=-x-3; 2x=-8, x= -4. hence sufficient

st.2

when x>-3
x+3=1 and x=-2 which is a valid solution
and when x<-3 we have
-x-3=1
x = -4 which is also a valid solution.
hence statement 2 alone is not sufficient

therefore A
Intern
Joined: 20 Apr 2017
Posts: 6
Re: What is the value of x?  [#permalink]

### Show Tags

18 Jul 2017, 04:11
Bunuel wrote:
What is the value of x?

(1) $$|x+5| = |x+3|$$ --> square both sides: $$(x+5)^2=(x+3)^2$$ --> $$x^2+10 x+25 = x^2+6 x+9$$ --> $$4x=-16$$ --> $$x=-4$$. Sufficient.

(2) $$|x+3| = 1$$ --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.

Hi Bunuel,

I got the answer A but just by plugging in numbers. I looked at the problem and saw that in order for |x+5| = |x+3| the difference has to be 2. Therefore |-1| = |1|.

|x+5| = 1, x = -4 or -6
|x+3| = 1, x = -4 or -2

We have one answer that fits both, therefore sufficient.
I had the same reasoning as you for statement (2).

Am I correct in my reasoning? I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?
Manager
Joined: 27 Jan 2016
Posts: 134
Schools: ISB '18
GMAT 1: 700 Q50 V34
Re: What is the value of x?  [#permalink]

### Show Tags

18 Jul 2017, 04:37
goodyear2013 wrote:
What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1

Stmt 1)
Three cases can be considered
i) x+5 = x+3 -> No x value can be derived
ii)x+5 = -(x+3) -> x=-4
iii)-(x+5) = x+3 -> x=-4

Hence suff

Stmt 2)
x+3=1 -> x=-2
x+3=-1 -> x=-4
2 values, hence insuff

Manager
Joined: 17 May 2015
Posts: 249
Re: What is the value of x?  [#permalink]

### Show Tags

18 Jul 2017, 08:19
1
tommh wrote:
Bunuel wrote:
What is the value of x?

(1) $$|x+5| = |x+3|$$ --> square both sides: $$(x+5)^2=(x+3)^2$$ --> $$x^2+10 x+25 = x^2+6 x+9$$ --> $$4x=-16$$ --> $$x=-4$$. Sufficient.

(2) $$|x+3| = 1$$ --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.

Hi Bunuel,

I got the answer A but just by plugging in numbers. I looked at the problem and saw that in order for |x+5| = |x+3| the difference has to be 2. Therefore |-1| = |1|.

|x+5| = 1, x = -4 or -6
|x+3| = 1, x = -4 or -2

We have one answer that fits both, therefore sufficient.
I had the same reasoning as you for statement (2).

Am I correct in my reasoning? I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?

Hi tommh,

Quote:
I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?

Yes, this is a standard method to solve such questions.

You can also solve this question using the modulus/absolute value definition.

Definition: Absolute value of a number is distance from 0.

Example: |x| = 3, we can write it as |x-0| = 3. x: those points whose distance from 0 is 3. So, on number line two points will satisfy the condition => x = -3 or 3

---------- -3-------------0-------------3--------------

Example2. |x+3| = 3, we can write it as |x- (-3)| = 3. x: those points whose distance from (-3) is 3 units => x = -6 or 0. Refer: (Example2.jpg)

Now, back to the question.

St.1: |x+5| = |x+3| . This can be written as |x - (-5)| = |x - (-3)|. x is number which is equidistant from (-5) and (-3). => x = -4. No other value will satisfy this condition. Please refer attached diagram (Statement1.jpg) . Hence, sufficient.

St2: |x+3| = 1. |x - (-3)| = 1 => x = -2 or -4. Not sufficient.

Hope it helps.

Thanks.
Attachments

Statement1.jpg [ 102.57 KiB | Viewed 741 times ]

Example2.jpg [ 78.57 KiB | Viewed 740 times ]

Intern
Joined: 20 Apr 2017
Posts: 6
Re: What is the value of x?  [#permalink]

### Show Tags

18 Jul 2017, 12:05
Thank you ganand, that makes sense.
Senior Manager
Joined: 15 Jan 2017
Posts: 351
Re: What is the value of x?  [#permalink]

### Show Tags

28 Jul 2017, 13:59
Value of X?
1) from this we get - 4 (keeping LHS and RHS negative and then reversing the same).
Substituting x has a constant value --> |-4 +5| =1 and |-4 +3|=1
SUFF (A)

2) |x+3|= 1
x= 4 and x= -4
substituting: |4+3| = 1 but not equal to 7 and |-4 +3| =1 so we have two values. Not suff.
Ans: A
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5783
Location: United States (CA)
Re: What is the value of x?  [#permalink]

### Show Tags

30 Jul 2017, 17:23
goodyear2013 wrote:
What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1

We need to determine the value of x.

Statement One Alone:

|x+5|=|x+3|

Since the two absolute value expressions are equal, we can solve for each situation: (1) when they are both positive and (2) when they have opposite signs.

(1) Both positive:

x + 5 = x + 3

We see that we do not get an answer for x.

(2) Opposite signs:

-(x + 5) = x + 3

-x - 5 = x + 3

-8 = 2x

-4 = x

We see x = -4. Statement one alone is sufficient to answer the question.

Statement Two Alone:

|x+3|=1

We can solve for each situation: (1) when (x + 3) is positive and (2) when (x + 3) is negative.

(1) (x + 3) is positive:

x + 3 = 1

x = -2

(2) (x + 3) is negative:

-x - 3 = 1

-x = 4

x = -4

We cannot determine a unique value for x.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Re: What is the value of x?   [#permalink] 30 Jul 2017, 17:23
Display posts from previous: Sort by