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## Comment on

Inequalities and Absolute Value## Is |x−1|<1|x−1|<1 ?

(1) (x−1)2≤1(x−1)2≤1

(2) x2−1>0

Could someone help me this?

## Are you sure you've correctly

Are you sure you've correctly transcribed the question?

Also, what's the source of this question?

Cheers,

Brent

## Hi Brent, have a query in the

https://gmatclub.com/forum/if-4-7-x-3-which-of-the-following-must-be-true-168681.html

If 4<(7-x)/3, which of the following must be true?

I. 5<x

II. |x+3|>2

III. -(x+5) is positive

(A) II only

(B) III only

(C) I and II only

(D) II and III only

(E) I, II and III

While I got the equations right, i.e in st2: x<-5 or x>-1 and st 3 is always true, the question asks which of the statement must be true and since st2 yields 2 possible solutions for x, the answer for me is B. Really confused how people have taken st2 to be always true.

## Question link: https:/

Question link: https://gmatclub.com/forum/if-4-7-x-3-which-of-the-following-must-be-tru...

Great question, Jalaj!

From the given information, we know for certain that x < -5

Given that x < -5, must statement II be true?

From statement II, you determined that EITHER x < -5 OR x > -1

So, if x < -5, must it be true that EITHER x < -5 OR x > -1?

In order to answer YES to the above question we only need one of the parts to be true: x < -5 OR x > -1

Since we can be certain that x < -5.

Notice that the question does NOT read "If x < -5, must it be true that BOTH x < -5 AND x > -1?"

Here's an analogous question:

Let's say you have a rock in your pocket, and someone asks you "Is it true that you have EITHER a rock in your pocket OR an elephant in your pocket?

The answer to that question is YES, it is true that I have EITHER a rock in my pocket OR an elephant in my pocket.

Does that help?

Cheers,

Brent

## Hi Brent, in the question

Therefore, x can have a value of -2, which negates the inequality question |x| > 3.

Therefore my answer is B. Can you help me identify where am I going wrong in this?

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

https://gmatclub.com/forum/if-x-3-which-of-the-following-must-be-true-138652-40.html

## Question link: https:/

Question link: https://gmatclub.com/forum/if-x-3-which-of-the-following-must-be-true-13...

Be careful! We cannot say "statement III has 2 possible solutions x < -1 AND x > 3"

The value of x cannot be less than -1 AND greater than 3 at the same time.

Instead, we can say that EITHER x < -1 OR x > 3

This is very similar to your question above.

I should also point out the error in your comment that "Therefore, x can have a value of -2, which negates the inequality question |x| > 3."

You are approaching this in the wrong direction.

We are told that it is 100% true that |x| > 3, and our job is to identify other statements (from I, II and III) that are 100% true.

Instead, you are assuming that statement III is true and trying to determine whether the given information (|x| > 3) is true.

Does this help?

Cheers,

Brent

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