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If |x|>3, which of the following must be true?

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Re: If |x| > 3 , which of the following must be true? [#permalink] New post 13 May 2013, 01:17
Archit143 wrote:
I too have the same doubt...can anyone address the query

Archit


The question asks is x>3 or x<-3?

III tells us that x>3 or x<-1. So is x>3 or x<-3? YES

x>3 from question => x>3from III: Correct
x<-3 from question => x<-1 from III: Correct as well. We are asked if x<-3 and III tells us that x<-1 so for sure it will be <-3 also.

Hope it's clear now!
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Re: If |x| > 3 , which of the following must be true? [#permalink] New post 13 May 2013, 08:44
Expert's post
danzig wrote:
If |x| > 3 , which of the following must be true?

I. x > 3

II. x^2 > 9

III. |x - 1| > 2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

I don't understand well III. |x - 1| > 2 is equivalent to x > 3 or x < -1. The last inequality (x < -1 ) includes integers -2 and -3, integers that are not included in one of the original inequalities ( x < -3 ). How could III be true? :?


If some numbers confuse you, don't fixate on them. Go ahead and take some other easier examples.
Let's keep the wording of the question same but make it simple.

If n < 6, which of the following must be true?

I.

II.

III. n < 8

Can we say that III must be true? Yes!
If n is less than 6 then obviously it is less than 8 too.
If n is less than 6, it will take values such as -20, 2, 5 etc. All of these values will be less than 8 too.

Values 6 and 7 are immaterial because n cannot take these values. You are given that n is less than 6 so you only need to worry about values that n CAN take. Those should satisfy n < 8.

Similarly, your question says that x > 3 or x < -3

Then we can say that x > 3 or x < -1. All values that will be less than -3 will be less than -1 too.

Check out my post on a similar tricky question : http://www.veritasprep.com/blog/2012/07 ... -and-sets/
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Re: If |x| > 3 , which of the following must be true? [#permalink] New post 13 Aug 2013, 12:40
What if x = -2 that is < -1 but > than -3 so IIImust be out?no




Zarrolou wrote:
Archit143 wrote:
I too have the same doubt...can anyone address the query

Archit


The question asks is x>3 or x<-3?

III tells us that x>3 or x<-1. So is x>3 or x<-3? YES

x>3 from question => x>3from III: Correct
x<-3 from question => x<-1 from III: Correct as well. We are asked if x<-3 and III tells us that x<-1 so for sure it will be <-3 also.

Hope it's clear now!


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Re: If |x|>3, which of the following must be true? [#permalink] New post 13 Aug 2013, 13:27
corvinis wrote:
If |x| > 3, which of the following must be true?

I. x > 3

II. X^2 > 9

III. |x-1|>2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

I can't understand how the official answer can be right. For me is B. Please respond and I'll provide official explanation! Thanks


|x| > 3 means x>3 or x<-3
so I is false because x<-3 is true.


II. x^2 > 9 satisfies both equations (use x=-4 or x=5 )

III. is also true for x=-4 and x=5.

so D
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Re: If |x| > 3 , which of the following must be true? [#permalink] New post 13 Aug 2013, 23:56
Expert's post
rusth1 wrote:
If |x| > 3, which of the following must be true?

I. x > 3
II. X^2 > 9
III. |x-1|>2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

What if x = -2 that is < -1 but > than -3 so IIImust be out?no




Zarrolou wrote:
Archit143 wrote:
I too have the same doubt...can anyone address the query

Archit


The question asks is x>3 or x<-3?

III tells us that x>3 or x<-1. So is x>3 or x<-3? YES

x>3 from question => x>3from III: Correct
x<-3 from question => x<-1 from III: Correct as well. We are asked if x<-3 and III tells us that x<-1 so for sure it will be <-3 also.

Hope it's clear now!


Image Posted from GMAT ToolKit


x cannot be -2 because we are told that |x|>3, and |-2|=2<3.

Hope it helps.
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Re: If |x|>3, which of the following must be true? [#permalink] New post 28 Oct 2014, 09:53
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Re: If |x|>3, which of the following must be true? [#permalink] New post 23 Nov 2014, 22:46
Hi All,

After going through the explanations I could understand why option B was not correct. But I am sure under timed conditions, I might make a similar mistake.
Does anyone have a way to solve such problems, so that a mistake can be avoided and an important case like the 3rd option be considered while evaluating answer choices?

Thanks,
AK
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Re: If |x|>3, which of the following must be true? [#permalink] New post 23 Nov 2014, 23:29
aj0809 wrote:
Hi All,

After going through the explanations I could understand why option B was not correct. But I am sure under timed conditions, I might make a similar mistake.
Does anyone have a way to solve such problems, so that a mistake can be avoided and an important case like the 3rd option be considered while evaluating answer choices?

Thanks,
AK



Hi AK,

Why will you leave an option out...that's a big no...in this question St 2 is true so you can remove answer options which don't have st 2 as one of the option and see if it reduces your work load...
You may want to refresh some basics on how to go about solving such questions..

This is why we need to practice and see where we are going wrong...For instance this is an important pointer for you to never to overlook an option..

Check out below link:
math-absolute-value-modulus-86462.html
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Re: If |x|>3, which of the following must be true? [#permalink] New post 23 Nov 2014, 23:43
Thanks WondedTiger,

Maybe I didn't present my question correctly. I didn't leave the 3rd option but came to the conclusion that it was wrong and chose my answer as B.
I just want to prevent that in timed conditions for difficult questions like these, which have subtle differences that makes an answer choice right.
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Re: If |x|>3, which of the following must be true? [#permalink] New post 23 Nov 2014, 23:53
aj0809 wrote:
Thanks WondedTiger,

Maybe I didn't present my question correctly. I didn't leave the 3rd option but came to the conclusion that it was wrong and chose my answer as B.
I just want to prevent that in timed conditions for difficult questions like these, which have subtle differences that makes an answer choice right.


hmm..

Did you solve the 3rd option correctly or you made it a mistake.
Identify the step where you made the mistake..
Consider making an error log..That will certainly help...
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Re: If |x|>3, which of the following must be true?   [#permalink] 23 Nov 2014, 23:53

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