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# What is x? (1) |x| < 2 (2) |x| = 3x – 2

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Manager
Joined: 11 Feb 2011
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What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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16 Jun 2011, 08:06
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47% (01:07) correct 53% (01:07) wrong based on 109 sessions

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What is x?

(1) |x| < 2

(2) |x| = 3x – 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/what-is-x-126874.html

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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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16 Jun 2011, 09:32
AnkitK wrote:
what is x?
A.|x|<2
B.|x|=3x-2

Sol:

Q: What is x?

1. -2<x<2
Not Sufficient.

2.
x=3x-2
2x=2
x=1

OR

-x=3x-2
4x=2
x=1/2
Not Sufficient.

Combining both;
1/2 and 1 both lie between -2<x<2
Not Sufficient.

Ans: "E"
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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16 Jun 2011, 09:34
Yeah i did the same but to my sorrow OA is B .
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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16 Jun 2011, 09:40
AnkitK wrote:
Yeah i did the same but to my sorrow OA is B .

B would be the answer if it is mentioned that x is an integer.
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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16 Jun 2011, 09:43
No not mentioned anywhere.Anyways thnkx for your response.
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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19 Jun 2011, 04:28
Because x = 1/2 doesn’t satisfy the second condition which is IxI= 3x-2. Therefore we are left with only one value, x=1.
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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05 Jul 2011, 06:41
AnkitK wrote:
what is x?
A.|x|<2
B.|x|=3x-2

A : insufficient

B : taking two scenarios when x< 0 and when x > 0

when x< 0 : -x=3x-2 --> x = 1/2 , this is not a valid solution since we assumed x<0 therefore the soulution is invalid.
when x>0 then x=3x-2 ---> x = 1 , this is a valid solution since we assumed that x > 0 , therefore Conditon B gives us a unique answer i.e. x= 1.
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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05 Jul 2011, 10:48
AnkitK wrote:
Yeah i did the same but to my sorrow OA is B .

i dont think that we need a condition " x must be an integer to get the answer B because
statement 1 is surely not sufficient.
statement 2 could be
case first: if x> 0 so x is 1
case secondL if x< so so x is 1/2 . this case should be eliminated becos x must be negative so if x=1/2 this case will be deleted....
thus x=1
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 03:18
2
1
AnkitK wrote:
what is x?
A.|x|<2
B.|x|=3x-2

You are missing an important point - let me explain.

We all know that if we have mods, we take two cases - positive and negative - and then solve the equation.
The point is - why do we do that?
If you remember, this is how we define mods

|x| = x if x is positive
and -x if x is negative

So basically, |x| takes different forms depending on whether x is positive or negative.
When I want to solve |x|=3x-2, I can't solve with |x|.

So I split it into two cases:
Case 1: x is positive
I get x = 3x - 2
x = 1
I accept this value of x since x has to be +ve and satisfy given equation. It does both.
Case 2: x is negative
-x = 3x - 2
x = 1/2
I reject this value since x should be negative for the equation to look like this.
So x can only take 1 value i.e. x = 1.

Remember, when you split |x| into two cases, you have to check that the value you get lies in the region in which you are expecting it to lie.
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 03:53
Good explanation VeritasPrepKarishma!
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 05:05
I think there is a flaw in above explanations

in case if x is negative then
we cannot say -x=3x-2
we should say -x= -3x -2
2x=-2 so x= -1
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 05:50

Statement 1 is insufficient
|x|<2
x>2
x<2
insufficient

Statement 2 insufficient
|x|=3x-2
X=1, 1/2

Both taken together
No single concise value as that is required for DS problems with value questions.

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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 06:03
AnkitK wrote:
what is x?
A.|x|<2
B.|x|=3x-2

St 1: X lies between -2 and 2 .. not sufficient

St2: X>0
X= 3x-2
-2x= -2
X =1 .. check if it satifies the equation
|1| = 3(1)-2 = 1 ... satisfies

X<0
-x = 3x-2
-4x = -2
x= 1/2 again check if satisfies the equation
|1/2| = 3(1/2)- 2 = -1/2 ... doesnt satisfy the equation
Hence X =1

Answer has to B . I dont think that the question requires to say that X is an integer.
only trick/tip here is : whenever there is Mod or Inequality , check the value whether it satifies the equation.
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 10:47
"I reject this value since x should be negative for the equation to look like this.
So x can only take 1 value i.e. x = 1."

im sorry but could you please explaine why you reject 1/2...
its also positive as 1
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 11:33
I dont know why is this question extended so much

Option A id definitely insufficient

Now in option B people are confused whether 1/2 can be a value of the x or not
But people ....try putting x=1/2 in the option B equation ....
l x l = 3x-2
therefore l 1/2 l = 3*1/2 -2
here l 1/2 l will be +ve ...i.e. 1/2
therefore 1/2 = 3/2 - 2 = (3-4)/2
hence 1/2 = - 1/2 ...which is not possible

similarly we even take x as -1/2 then also the resulting values come as 1/2 = - 7/2 ...again unequal ....

Hence x can take only one value and that is 1

Hence ans has to be B
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 21:07
getmydream wrote:
I think there is a flaw in above explanations

in case if x is negative then
we cannot say -x=3x-2
we should say -x= -3x -2
2x=-2 so x= -1

In case x is negative, 3x does not change to -3x. When we write 'x', the negative sign is already included.
But when x is negative, |x| becomes -x. The reason is that |x| can never be negative. If x is negative, -x makes it positive.
e.g.
If x = -4
|x| = |-4| = 4 which is actually -x = -(-4) = 4
Hence |x| = -x when x is negative.
When x is positive, |x| = x
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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06 Jul 2011, 21:16
1
Galiya wrote:
"I reject this value since x should be negative for the equation to look like this.
So x can only take 1 value i.e. x = 1."

im sorry but could you please explaine why you reject 1/2...
its also positive as 1

Let me highlight the main points:
|x| = x if x is positive
and [highlight]|x| = -x if x is negative[/highlight] (As explained in the reply above)

Case 1: x is positive
|x|=3x-2 becomes x=3x-2
When I solve this, I get x = 1. This is acceptable since here I am working on the case where x is positive.

[highlight]Case 2: x is negative[/highlight]
[highlight]|x|[/highlight]=3x-2 becomes [highlight]-x[/highlight]= 3x - 2
Now I solve and get a value of x. This value will be acceptable only if it is negative since I am working on the case where x is negative. But when I solve, I get x = 1/2. It is not negative so I reject it.

To test, try and put x = 1 in |x|=3x-2
It satisfies.

Put x = 1/2 in |x|=3x-2
It doesn't satisfy.
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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07 Jul 2011, 04:24
Thanks Karishma for the explanation >
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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08 Jul 2011, 10:37
AnkitK wrote:
what is x?
A.|x|<2
B.|x|=3x-2

B for me (X>0 And x=1)
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Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2  [#permalink]

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08 Jul 2011, 20:31
1. Not sufficient
-2<x<2

2. Sufficient

when x>=0, x =3x-2 => x =1
when x<0 , -x=3x-2 => x =1/2 , but this is not valid as x<0.

so x can only be 1.

Re: What is x? (1) |x| < 2 (2) |x| = 3x – 2 &nbs [#permalink] 08 Jul 2011, 20:31

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