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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, 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] 13 Aug 2013, 23:56
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