Pls help solve this.

Question

Attached is an absolute value inequation question from Pack1. I am confused with the explanation provided in the official Answer. Please help me resolve this.

GMATGuruNY · Answer

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

1) x > 3
2) x^2 > 9
3) |x - 1| > 2

I only
II only
I and II only
II and III only
I, II, and III

Plug in a value that satisfies the condition that |x| > 3.
Let x=-4.
Eliminate any statement that is not valid for x=-4.

Statement I: x > 3
-4 > 3
Not true.
Eliminate any answer choice that includes I.
Eliminate A, C and E.

Compare the remaining answer choices.
B and D each include II.
Thus, II must be true, since it is included in both of the remaining answer choices.
Thus, we need to evaluate only statement III.

Statement III: |x-1| > 2
|x-1| > 2 implies that the distance between x and 1 is more than 2 units.
|x| > 3 implies that x is more that 3 units from 0.
Since x is more than 3 units from 0 -- in other words, x<-3 or x>3 -- the distance between x and 1 must be more than 2 units.
Thus, III must be true.
Eliminate B, which doesn't include III.

The correct answer is D.

Please note the following:
If |x| > 3, then statement III must be true: |x-1| > 2.
This does NOT imply the reverse.
If |x-1| > 2, it does NOT have to be true that |x| > 3.
For example, x=-2 satisfies |x-1| > 2 but not |x| > 3.

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theCodeToGMAT · Answer

Given |x|>3 ... this means

If X is positive then .. x > 3

If X is negative then .. x < -3

3 < x < -3

Statement 1: NOT TRUE.
Statement 2: True For any value of x as per the above range
Statement 3: True For any value of X as per the above range

Answer [D]

ani781 · Answer

Statement 3: True For any value of X as per the above range

Hi Rahul,
3 implies two cases: a) x>3 or b) x<-1
How come , case (b) suffice... x is in the range < -3 or > +3, but x as per case (b) is anything less than -1 , so -2 also can be the value.

Can you pls explain.

theCodeToGMAT · Answer

ani781 wrote:Statement 3: True For any value of X as per the above range Hi Rahul, 3 implies two cases: a) x>3 or b) x<-1 How come , case (b) suffice... x is in the range < -3 or > +3, but x as per case (b) is anything less than -1 , so -2 also can be the value. Can you pls explain. Ani, you are neglecting the "given"; we are provided that |x|>3 that means either x>3 or x <-3 Case b) says that x < -1 .. so any number lesser than -3 will surely be lesser than -1.. hence this case is sufficient...as all the given values are satisfied... However, if the scenario were: given x < -1 and and the case results in x < -6 then the same inference was not applicable..as any number lesser than -1 is not surely lesser than -6// for example -2

Rich.C@EMPOWERgmat.com · Answer

Hi Ani781,

In Roman Numeral questions, usually the fastest way to get to the correct answer is to DISPROVE what the question is asking for:

Here, we're told that |x| > 3

This means that x COULD BE > 3 OR x COULD BE < -3

We can use this information to eliminate options since the prompt asks what MUST be true.

I. x > 3

We can see that x COULD BE a negative (anything less than -3), so I doesn't have to be true.
Eliminate A, C and E

You'll now notice that II is in both of the remaining answers, so we don't even need to look at it.

III. |x-1| > 2

This is a tough concept for many people to deal with, so let's make things easier and just figure out which values fit this.

We know from the prompt that x CAN be > 3
On the "positive" side, x > 3 would "fit" this.

We also know from the prompt that x CAN be < -3
On the "negative" side, x < -3 also would "fit this.

So, III is TRUE

Final answer: D

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