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# What is the value of x?

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Intern
Joined: 19 Apr 2015
Posts: 13
What is the value of x?  [#permalink]

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Updated on: 18 Nov 2015, 00:10
6
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:39) correct 30% (01:40) wrong based on 254 sessions

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What is the value of x?

(1) |x + 2| = 2|x - 2|
(2) x > 2

My answer is A.Want to understand how to tackle mod values. Thanks

Originally posted by aby0007 on 17 Nov 2015, 23:23.
Last edited by Bunuel on 18 Nov 2015, 00:10, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Aug 2009
Posts: 7212
Re: What is the value of x?  [#permalink]

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18 Nov 2015, 00:47
1
1
aby0007 wrote:
What is the value of x?

(1) |x + 2| = 2|x - 2|
(2) x > 2

My answer is A.Want to understand how to tackle mod values. Thanks

Hi aby0007,
why the answer cannot be A is related to what you have asked ' how to tackle mod values'..

lets see the mod Eq..
(1) |x + 2| = 2|x - 2|..
so here we have 2 mods and we will have 4 eqs where each mod takes +ive and -ive values..
a) x+2=2(x-2)..(both +ive)
x=6..
b)-(x+2)=-2(x-2)..(both -ive)
-x-2=-2x+4..
again x=6..
c)x+2=-2(x-2)..(one +ive and one -ive)
x=2/3...
d)-(x+2)=2(x-2)..(one +ive and one -ive)
x=2/3..

two different values of x so insuff...

(2) x > 2
innumerable values... 3,4,9/2..etc... so insuff

combined.. only one value of x, which suffices the two conditions..
x=6..suff
C
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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?  [#permalink]

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18 Nov 2015, 00:52
1
x = ?
St1: |x + 2| = 2|x - 2|
Square both sides: (x+2)^2 = 4(x-2)^2
x^2 + 4x + 4 = 4(x^2 - 4x + 4)
3x^2 - 20x + 12 = 0
Solving we get, x = 6 or 2/3
Statement 1 alone is not sufficient

St2: x > 2 --> Clearly not sufficient

Combining St1 and St2, we get x = 6.

Intern
Joined: 19 Apr 2015
Posts: 13
Re: What is the value of x?  [#permalink]

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18 Nov 2015, 00:59
Thanks chetan and Vyshak , got it now.
Intern
Joined: 30 Nov 2015
Posts: 9
Re: What is the value of x?  [#permalink]

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10 Dec 2015, 12:56
Vyshak wrote:
x = ?
St1: |x + 2| = 2|x - 2|
Square both sides: (x+2)^2 = 4(x-2)^2
x^2 + 4x + 4 = 4(x^2 - 4x + 4)
3x^2 - 20x + 12 = 0
Solving we get, x = 6 or 2/3
Statement 1 alone is not sufficient

St2: x > 2 --> Clearly not sufficient

Combining St1 and St2, we get x = 6.

I wonder, is this a good strategy for all absolute value questions? Squaring the absolute value equations? Or should I be careful in applying this for certain scenarios?
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Joined: 02 Aug 2009
Posts: 7212
Re: What is the value of x?  [#permalink]

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10 Dec 2015, 17:47
daisuke123 wrote:
Vyshak wrote:
x = ?
St1: |x + 2| = 2|x - 2|
Square both sides: (x+2)^2 = 4(x-2)^2
x^2 + 4x + 4 = 4(x^2 - 4x + 4)
3x^2 - 20x + 12 = 0
Solving we get, x = 6 or 2/3
Statement 1 alone is not sufficient

St2: x > 2 --> Clearly not sufficient

Combining St1 and St2, we get x = 6.

I wonder, is this a good strategy for all absolute value questions? Squaring the absolute value equations? Or should I be careful in applying this for certain scenarios?

Hi,
it would be best to put each mod as +ive and -ive valus and solve for all the combuinations of number of mods there..
_________________

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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Joined: 30 Nov 2015
Posts: 9
Re: What is the value of x?  [#permalink]

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11 Dec 2015, 13:11
chetan2u wrote:
daisuke123 wrote:
Vyshak wrote:
x = ?
St1: |x + 2| = 2|x - 2|
Square both sides: (x+2)^2 = 4(x-2)^2
x^2 + 4x + 4 = 4(x^2 - 4x + 4)
3x^2 - 20x + 12 = 0
Solving we get, x = 6 or 2/3
Statement 1 alone is not sufficient

St2: x > 2 --> Clearly not sufficient

Combining St1 and St2, we get x = 6.

I wonder, is this a good strategy for all absolute value questions? Squaring the absolute value equations? Or should I be careful in applying this for certain scenarios?

Hi,
it would be best to put each mod as +ive and -ive valus and solve for all the combuinations of number of mods there..

Thank you, I'm just thinking of alternative strategies. Just a thought.
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Re: What is the value of x?  [#permalink]

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13 Dec 2015, 16:37
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of x?

(1) |x + 2| = 2|x - 2|
(2) x > 2

-> In the original condition, there is 1 variable(x), which should match with the number of equation. So, you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
In 1), x+2=-2(x-2), x+2=-2x+4, 3x=2, x=2/3 or x+2=2(x-2)=2x-4, x=6, which is not unique and therefore not sufficient.
In 2), it is not unique and therefore not sufficient.
In 1) & 2), as x=6, which is unique and therefore sufficient. Therefore, the answer is C.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Joined: 27 Oct 2015
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Re: What is the value of x?  [#permalink]

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13 Dec 2015, 18:07
The first statement alone cannot give us the value of x. Not sufficient and hence options A, D are ruled out
The second statement alone cannot give us the value of X. not sufficient and hence option B is ruled out

We are left with Options C and E
If we combine the 2 statements then we know that x > 2 and the modulus signs in statement one can be converted to brackets
We can solve for x

Hence C [we don't have to solve the problem ]
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Re: What is the value of x?  [#permalink]

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30 Mar 2017, 06:13
aby0007 wrote:
What is the value of x?

(1) |x + 2| = 2|x - 2|
(2) x > 2

My answer is A.Want to understand how to tackle mod values. Thanks

Statement 1 will give two value of x. one positive (6) and one negative hence insufficient
Statement 2 is also insufficient because x could be any thing greater than 2
combining 1 and 2 together we get only one value of x that is greater than 2
hence together sufficient.
Hence C
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Re: What is the value of x?  [#permalink]

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30 Mar 2017, 10:30
daboo343 wrote:
aby0007 wrote:
What is the value of x?

(1) |x + 2| = 2|x - 2|
(2) x > 2

My answer is A.Want to understand how to tackle mod values. Thanks

Statement 1 will give two value of x. one positive (6) and one negative hence insufficient
Statement 2 is also insufficient because x could be any thing greater than 2
combining 1 and 2 together we get only one value of x that is greater than 2
hence together sufficient.
Hence C

Trust a typo error.
Statement 1 will give two positive values, 6 and 2/3
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Re: What is the value of x? &nbs [#permalink] 30 Mar 2017, 10:30
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