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What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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24 Apr 2017, 04:21
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What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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Joined: 26 Mar 2013
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What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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24 Apr 2017, 14:04
Wereheretotakeover wrote: Hi,
please correct me if I'm wrong.
Statement 1: 2x − 1 = 3x + 6
equals: 2x1 = 3x+6 x=7
2x1 = (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.




Intern
Joined: 20 Apr 2017
Posts: 4

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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24 Apr 2017, 04:33
Hi,
please correct me if I'm wrong.
Statement 1: 2x − 1 = 3x + 6
equals: 2x1 = 3x+6 x=7
2x1 = (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
Joined: 05 Mar 2015
Posts: 995

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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24 Apr 2017, 11:00
Wereheretotakeover wrote: Hi,
please correct me if I'm wrong.
Statement 1: 2x − 1 = 3x + 6
equals: 2x1 = 3x+6 x=7
2x1 = (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 Wereheretotakeoveryour solution is not correct 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
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24 Apr 2017, 14:07
Mo2men wrote: Wereheretotakeover wrote: Hi,
please correct me if I'm wrong.
Statement 1: 2x − 1 = 3x + 6
equals: 2x1 = 3x+6 x=7
2x1 = (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
Joined: 09 Apr 2017
Posts: 8

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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24 Apr 2017, 22:39
rohit8865 wrote: Wereheretotakeover wrote: Hi,
please correct me if I'm wrong.
Statement 1: 2x − 1 = 3x + 6
equals: 2x1 = 3x+6 x=7
2x1 = (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 Wereheretotakeoveryour 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.



Director
Joined: 05 Mar 2015
Posts: 995

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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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: 2x1 = 3x+6 x=7
2x1 = (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 Wereheretotakeoveryour 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..........



Manager
Joined: 17 Aug 2012
Posts: 123
Location: India
Concentration: General Management, Strategy
GPA: 3.75
WE: Consulting (Energy and Utilities)

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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25 Apr 2017, 09:04
statement 1 2x − 1 = 3x + 6 For X> 1/2 ; 2X1 =3X + 6 X= 7 BUT X>1/2 hence not possible For X<1/2 ; 2X1 = 3X  6 X=1 OK Only one solution Statement 2 : two value of x hence no solution Answer A



Director
Joined: 12 Nov 2016
Posts: 713
Location: United States
GPA: 2.66

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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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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Joined: 05 Jul 2017
Posts: 512
Location: India
GPA: 4

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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08 Sep 2017, 22:33
Hey BunuelI 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/whatisx12 ... l#p1037498) Statement I:  2x − 1 = 3x + 6 LHS is nonnegative, therefore RHS should alos be nonnegative 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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Posts: 56303

Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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08 Sep 2017, 22:42
pikolo2510 wrote: Hey BunuelI 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/whatisx12 ... l#p1037498) Statement I:  2x − 1 = 3x + 6 LHS is nonnegative, therefore RHS should alos be nonnegative 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
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09 Sep 2017, 11:56
Bunuel wrote: pikolo2510 wrote: Hey BunuelI 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/whatisx12 ... l#p1037498) Statement I:  2x − 1 = 3x + 6 LHS is nonnegative, therefore RHS should alos be nonnegative 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
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25 Sep 2018, 13:24
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 lefthand 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
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30 May 2019, 01:55
Bunuel can you please share the official solution!




Re: What is the value of x? (1) 2x − 1 = 3x + 6 (2) x^2 = 1
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30 May 2019, 01:55






