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What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1

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What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1 [#permalink]

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New post 24 Apr 2017, 04:21
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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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New post 24 Apr 2017, 04:33
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

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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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New post 24 Apr 2017, 11:00
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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

your solution is not correct

Ans is A

try again :)

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What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1 [#permalink]

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New post 24 Apr 2017, 14:04
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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.

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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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New post 24 Apr 2017, 14:07
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

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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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New post 24 Apr 2017, 22:39
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

your solution is not correct

Ans is A

try again :)


Answer should be D.

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.

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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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New post 24 Apr 2017, 22:46
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

your solution is not correct

Ans is A

try again :)


Answer should be D.

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..........

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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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New post 25 Apr 2017, 09:04
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

Answer 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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New post 01 Sep 2017, 19:14
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

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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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New post 08 Sep 2017, 22:33
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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Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1 [#permalink]

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New post 08 Sep 2017, 22:42
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Expert's post
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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Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1 [#permalink]

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New post 09 Sep 2017, 11:56
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] 09 Sep 2017, 11:56
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