If |2z| – 1 ≥ 2, which of the following graphs could be a number line

Question

If |2z| – 1 ≥ 2, which of the following graphs could be a number line representing all the possible values of z? https://gmatclub.com/forum/download/file.php?id=41206 2A8vkix.jpg

amandeep0306 · Answer

|2z|-1 >= 2 
|2z| >= 3
|z| >= 3/2
so it means z>= 3/2 or z<= -3/2

option :- A

Mansoor50 · Answer

Hi......since its an OR thing, why ignore abs(2z) -1 < -2?

this gives x--> 1/2 an -1/2

regards

KarishmaB · Answer

|2z| – 1 ≥ 2

|2z| ≥ 3

|z| ≥ 3/2

So  z \geq 1.5  or  z \leq -1.5

Answer (A)

nsdl1985 · Answer

Option A and Option D are same?

Bunuel · Answer

No. Notice the bolded parts in those options. A reads:  x \leq -1  or  x \geq 1 , while D reads  -1 \leq x \leq 1 .

nsdl1985 · Answer

Thanks a lot Bunuel. Lots of love and blessings to you for helping all of us here on Gmatclub.

BrentGMATPrepNow · Answer

IMPORTANT: This question is similar to "What must be true" questions. The difference is that the correct answer choice shows every possible solution (and no more) to be given inequality.

Let's TEST SOME values.

When I scan the answer choices, I see that some have 0 as part of the solution, and others don't. 
So, let's see what happens when   z = 0

Plug   z = 0   into original equation to get: |2(  0  )| – 1 ≥ 2
Evaluate to get: |0| – 1 ≥ 2
We get: 0 – 1 ≥ 2
And then: -1 ≥ 2
NOT TRUE.
So,   z = 0   is  NOT  a solution. 
Therefore, we'll ELIMINATE D and E, since they say z=0  IS  a solution.

Strategy: Among the three remaining answer choices, two have have 1 as part of the solution, and one doesn't.   
So, let's see what happens when   z = 1  
Plug   z = 1   into original equation to get: |2(  1  )| – 1 ≥ 2
Evaluate to get: |2| – 1 ≥ 2
We get: 2 – 1 ≥ 2
And then: 1 ≥ 2
NOT TRUE.
So,   z = 1   is  NOT  a solution to the given inequality. 
Therefore, we'll ELIMINATE B and C, since they say z = 1  IS  a solution.

By the process of elimination, we're left with A, the correct answer.

Cheers,
Brent

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If |2z| – 1 ≥ 2, which of the following graphs could be a number line

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If |2z| – 1 ≥ 2, which of the following graphs could be a number line

Prep Toolkit

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