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what is x? A.|x|<2 B.|x|=3x-2 [#permalink]
 16 Jun 2011, 08:06
Question Stats:
35% (01:47) correct
65% (00:42) wrong based on 0 sessions
what is x? A.|x|<2 B.|x|=3x-2
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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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Yeah i did the same but to my sorrow OA is B .
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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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No not mentioned anywhere.Anyways thnkx for your response.
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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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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. Hence the answer is B.
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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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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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Good explanation VeritasPrepKarishma!
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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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Answer is E 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.  Posted from GMAT ToolKit
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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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"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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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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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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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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Thanks Karishma for the explanation >
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AnkitK wrote: what is x?
A.|x|<2
B.|x|=3x-2 B for me (X>0 And x=1) 
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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.
Answer is B.
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