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

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CEO
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Re: If |x|>3, which of the following must be true?  [#permalink]

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New post 06 Feb 2018, 11:44
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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


If |x| > 3, then it must be true that EITHER x > 3 OR x < -3

(1) x > 3
This need not be true, since it's also possible that x < -3.
For example, x COULD equal -5
So, statement I need not be true.
ELIMINATE answer choice A, C and E

(2) x² > 9
This means that EITHER x > 3 OR x < -3
Perfect - this matches our original conclusion that EITHER x > 3 OR x < -3


(3) |x-1| > 2
Let's solve this further.
We get two cases:
case a) x - 1 > 2, which means x > 3 PERFECT
or
case b) x - 1 < -2, which means x < -1
Must it be true that x < -1?
YES.
We already learned that EITHER x > 3 OR x < -3
If x < -3, then we can be certain that x < -1
For example, if I tell you that the temperature is less than -3 degrees Celsius, can we be certain that the temperature is less than -1 degrees? Yes.
So, statement 3 must also be true.

Answer: D

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com
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If |x|>3, which of the following must be true?  [#permalink]

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New post 20 Feb 2018, 23:32
Since it is give that |x| > 3, we can take two values of x: 4 and -4.

Only II and III are true.

Is this really a 700 level question?
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If |x|>3, which of the following must be true?  [#permalink]

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New post 07 Mar 2018, 16:47
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

Main Idea: We need to use the normal expressions corresponding to the modulus expression given and solve for x and compare with the choices given for truth of the choices.

Details: By topic specific problem solving aid , which is :

- For converting the modulus to the normal form, one would be just remove the modulus and the other would be to remove the modulus and add a negative sign before the expression. For example |x-3| can correspond to (x-3) or –(x-3).
, we have

X >3 or x<-3

Checking the choices we see:

(i) Need not be true
(ii) must be true
(iii) implies x-1>2 => x>3 or –(x-1) >2 => x<-1. This is consistent with what is given. Hence true
Hence D.
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Re: If |x|>3, which of the following must be true?  [#permalink]

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New post 26 Sep 2018, 11:15
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


The key to correctly answering such questions is that the inequations/equations that we are evaluating, the answer range should be a Super Set of the given range.
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If my post was of any help to you, You can thank me in the form of Kudos!!

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Re: If |x|>3, which of the following must be true? &nbs [#permalink] 26 Sep 2018, 11:15

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