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# What is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 51067
What is the value of x?  [#permalink]

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25 Mar 2015, 02:59
2
10
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:35) correct 35% (02:01) wrong based on 357 sessions

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What is the value of x?

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

(2) |5x + 3| = 2x + 9

Kudos for a correct solution.

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Senior Manager
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Re: What is the value of x?  [#permalink]

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25 Mar 2015, 05:31
Bunuel wrote:
What is the value of x?

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

(2) |5x + 3| = 2x + 9

Kudos for a correct solution.

Statement 1:
6-3x=x-2
x=2

6-3x=-x+2
x=2
Sufficient

Statement 2:
5x+3=2x+9
x=2

5x+3=-2x-9
x= -12/7
Insufficient

Manager
Joined: 11 Sep 2013
Posts: 109
Re: What is the value of x?  [#permalink]

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26 Mar 2015, 02:32
1
1
(1) |6 - 3x| = x - 2

x-2 must be positive => x>2 => ||6 - 3x|=3x-6 => Just have one value of x => Suff

|5x + 3| = 2x + 9

x must be over -9/2 => 5x+3 can be positive or negative => Having 2 values of x => Insufficient

Director
Joined: 21 May 2013
Posts: 653
Re: What is the value of x?  [#permalink]

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28 Mar 2015, 07:59
Bunuel wrote:
What is the value of x?

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

(2) |5x + 3| = 2x + 9

Kudos for a correct solution.

1. 6-3X=X-2
X=2
OR
-6+3X=X-2
X=2. Statement 2 is sufficient
2. 5x+3=2x+9
x=2
OR
-5X-3=2X+9
7X=-12
X=-12/7. Statement 2 is Insufficient
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Re: What is the value of x?  [#permalink]

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30 Mar 2015, 02:59
1
I simply solved the 2 eqs. is there any better sol?
My sol :
1) |6x-3| = 6x-3 or -6x+3.
Thus putting in eq 1 : 6x-3=x-2 gives x = 2. Similarly, -6x+3=x-2 gives x=2. Thus we get a value for x. SUFF.

2) |5x+3| = 5x+3 or -5x-3.
Solving Similarly I got 2 diff values of x = 2 or -12/7. Thus NS.

Hence A.
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Kudos!!

Math Expert
Joined: 02 Sep 2009
Posts: 51067
Re: What is the value of x?  [#permalink]

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30 Mar 2015, 03:56
1
1
Bunuel wrote:
What is the value of x?

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

(2) |5x + 3| = 2x + 9

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

absolutes_text.png [ 12.37 KiB | Viewed 2460 times ]

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Intern
Joined: 27 Sep 2017
Posts: 10
Re: What is the value of x?  [#permalink]

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15 Feb 2018, 10:55
Hello chetan2u,

I Read your post about the absolute Modulus and accordingly I tried to solve this problem by critical value method. Hereunder my solution and please correct me if I did something wrong.

Statement1:-
the critical value is 2 so we are looking for values : x>=2 or x<2.

x>=2
If x>=2 ,let x=3 for example , the modulus would be negative. so by assigning -ive sign to the modulus we will get -(6-3x)=x-2 , so x=2, which is in the region x>=2 so we will accept this value.

x<2
If x<2, let x=-3 for example , the modulus would be positive. so by assigning +ve sign to the modulus we will get (6-3x)=x-2 , so x=2, which is not in the region x<2 , so this value is rejected.

The same as for Statement 2 , the critical value is -3/5 . so x>=-3/5 or x<-3/5 after solving it we will get 2 values , one accepted "x=2" and one rejected x=-12/17
Math Expert
Joined: 02 Aug 2009
Posts: 7097
Re: What is the value of x?  [#permalink]

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15 Feb 2018, 20:09
ahmed.abumera wrote:
Hello chetan2u,

I Read your post about the absolute Modulus and accordingly I tried to solve this problem by critical value method. Hereunder my solution and please correct me if I did something wrong.

Statement1:-
the critical value is 2 so we are looking for values : x>=2 or x=2
If x>=2 ,let x=3 for example , the modulus would be negative. so by assigning -ive sign to the modulus we will get -(6-3x)=x-2 , so x=2, which is in the region x>=2 so we will accept this value.

x=-3/5 or x<-3/5 after solving it we will get 2 values , one accepted "x=2" and one rejected x=-12/17

hi,
you have found all other values correct but there is one problem..
|5x + 3| = 2x + 9...
take x as x<-3/5 and you have got an answer -12/17..
now -12/17 <-3/5..
so this is also accepted..
so two values for statement II hence insuff..

otherwise this is what you are required to do in a proper method
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the value of x? &nbs [#permalink] 15 Feb 2018, 20:09
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