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Math Expert V
Joined: 02 Sep 2009
Posts: 56303
What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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14 00:00

Difficulty:   85% (hard)

Question Stats: 41% (01:36) correct 59% (01:12) wrong based on 271 sessions

### HideShow timer Statistics What is the value of x?

(1) |2x − 1| = 3x + 6
(2) x^2 = 1

_________________
SVP  V
Joined: 26 Mar 2013
Posts: 2284
What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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5
1
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Hi Max,

When you deal with such statement, you need to add extra step. You need to check the solutions you get in the original equation.

x =-7, substitute in original equation: |2x − 1| = 3x + 6

|-14 − 1| = -21 + 6......15=-15.........so, x=-7 is not viable solution.

x=-1
|- 3| = 3........3=3..............so x=-1 is viable solution

So we have only one answer.
##### General Discussion
Intern  Joined: 20 Apr 2017
Posts: 4
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max
Director  D
Joined: 05 Mar 2015
Posts: 995
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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1
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max

hi Wereheretotakeover

Ans is A

try again Intern  Joined: 20 Apr 2017
Posts: 4
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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Mo2men wrote:
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Hi Max,

When you deal with such statement, you need to add extra step. You need to check the solutions you get in the original equation.

x =-7, substitute in original equation: |2x − 1| = 3x + 6

|-14 − 1| = -21 + 6......15=-15.........so, x=-7 is not viable solution.

x=-1
|- 3| = 3........3=3..............so x=-1 is viable solution

So we have only one answer.

Hi,

thank you very much! Completely forgot about it.

Greetings
Max
Intern  B
Joined: 09 Apr 2017
Posts: 8
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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rohit8865 wrote:
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max

hi Wereheretotakeover

Ans is A

try again Statement 2 gives us 2 values for x: 1 & -1

Following the same method used for Statement 1, x = 1 does not give us a solution. Hence, -1 is the solution.
Director  D
Joined: 05 Mar 2015
Posts: 995
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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koolhunk wrote:
rohit8865 wrote:
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max

hi Wereheretotakeover

Ans is A

try again Statement 2 gives us 2 values for x: 1 & -1

Following the same method used for Statement 1, x = 1 does not give us a solution. Hence, -1 is the solution.

i think u got confused over what question asked!!!!!!

Happy learning..........
Manager  S
Joined: 17 Aug 2012
Posts: 123
Location: India
Concentration: General Management, Strategy
Schools: Copenhagen, ESMT"19
GPA: 3.75
WE: Consulting (Energy and Utilities)
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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statement 1 2x − 1| = 3x + 6
For X> 1/2 ; 2X-1 =3X + 6
X= -7 BUT X>1/2 hence not possible
For X<1/2 ; 2X-1 = -3X - 6
X=-1 OK
Only one solution

Statement 2 : two value of x hence no solution

Director  S
Joined: 12 Nov 2016
Posts: 713
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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1
Bunuel wrote:
What is the value of x?

(1) |2x − 1| = 3x + 6
(2) x^2 = 1

Have to be careful with the algebra here

Stmnt 1

2x- 1 = 3x + 6
-1= x + 6
x = -7

-l2x -1l = 3x + 6
-2x + 1 = 3x +6
1= 5x +6
-5 =5x
x = -1

Be careful- only negative one satisfies the equation so x= -7 cannot be a value of X

Suff

Stmnt 2

X^2= 1
x= -1 , 1

Insuff

A
BSchool Forum Moderator P
Joined: 05 Jul 2017
Posts: 512
Location: India
GMAT 1: 700 Q49 V36 GPA: 4
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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Hey Bunuel

I need some help. I'm going wrong somewhere but I can't identify where. Below are the steps :-
(I'm trying to follow the same steps you used here in this post https://gmatclub.com/forum/what-is-x-12 ... l#p1037498)

Statement I: -
|2x − 1| = 3x + 6
LHS is non-negative, therefore RHS should alos be non-negative

3x+6>=0
x>= -2

2x − 1 = 3x + 6
Solving the above equation, we get
x= -7
We should discard this value as -7 < -2. For RHS to be positive we need something >= -2

How do I proceed ahead after this step? I want to use the conceptual method you used in the post I mentioned above. Please help. Thanks
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Math Expert V
Joined: 02 Sep 2009
Posts: 56303
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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2
pikolo2510 wrote:
Hey Bunuel

I need some help. I'm going wrong somewhere but I can't identify where. Below are the steps :-
(I'm trying to follow the same steps you used here in this post https://gmatclub.com/forum/what-is-x-12 ... l#p1037498)

Statement I: -
|2x − 1| = 3x + 6
LHS is non-negative, therefore RHS should alos be non-negative

3x+6>=0
x>= -2

2x − 1 = 3x + 6
Solving the above equation, we get
x= -7
We should discard this value as -7 < -2. For RHS to be positive we need something >= -2

How do I proceed ahead after this step? I want to use the conceptual method you used in the post I mentioned above. Please help. Thanks

You cannot use this method here becasue not for all values of x which are >= -2, the expression in the modulus (2x − 1) is positive.

In the problem you refer to we have |x| = 3x – 2. RHS must be >= 0, so x >= 2/3. Now, if x >= 2/3, then |x| = x, so we can write x = 3x - 2, which is not the case for the problem above.
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Joined: 05 Jul 2017
Posts: 512
Location: India
GMAT 1: 700 Q49 V36 GPA: 4
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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Bunuel wrote:
pikolo2510 wrote:
Hey Bunuel

I need some help. I'm going wrong somewhere but I can't identify where. Below are the steps :-
(I'm trying to follow the same steps you used here in this post https://gmatclub.com/forum/what-is-x-12 ... l#p1037498)

Statement I: -
|2x − 1| = 3x + 6
LHS is non-negative, therefore RHS should alos be non-negative

3x+6>=0
x>= -2

2x − 1 = 3x + 6
Solving the above equation, we get
x= -7
We should discard this value as -7 < -2. For RHS to be positive we need something >= -2

How do I proceed ahead after this step? I want to use the conceptual method you used in the post I mentioned above. Please help. Thanks

You cannot use this method here becasue not for all values of x which are >= -2, the expression in the modulus (2x − 1) is positive.

In the problem you refer to we have |x| = 3x – 2. RHS must be >= 0, so x >= 2/3. Now, if x >= 2/3, then |x| = x, so we can write x = 3x - 2, which is not the case for the problem above.

Got it, Thanks a ton Bunuel!
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Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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2
For the first statement you need to use the two case approach for absolute values.

|2x−1|=3x+6 means that: 3x+6 could equal 2x−1, in which case:
x=−7
or, 3x+6 could equal −(2x−1) in which case:
3x+6=−2x+1, so
5x=−5
and therefore:

x=−1
So with two possible values it would be very tempting to say that statement 1 is not sufficient, then recognize that while statement 2 is clearly not sufficient on its own, it eliminates x=−7as a possibility when you use the two statements together. But wait!

If you return to your work from statement 1 to plug your solutions back in for a quick logic test, you'll see that −7 is an extraneous solution: |2(−7)−1|=3(−7)+6
means that:

|−15|=−15

Which does not work, since the absolute value on the left means that the left-hand side will be POSITIVE 15, while the right is stuck at NEGATIVE 15. This is known as an extraneous solution, and is why the process for solving absolute values always includes the step "plug your solutions back into the equation to verify that they are valid." Here, since −7 is invalid, statement 1 guarantees that x=−1 is the sole solution, and statement 1 is therefore sufficient. The correct answer is A.
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Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

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Bunuel can you please share the official solution! Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1   [#permalink] 30 May 2019, 01:55
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