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Intern  B
Joined: 22 Mar 2017
Posts: 15
Is −2 < z < 2?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 68% (01:20) correct 32% (01:39) wrong based on 75 sessions

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Is −2 < z < 2?

(1) z^2 < 4

(2) z^2 > −4

Originally posted by Nathanlambson on 07 Jun 2017, 15:43.
Last edited by Bunuel on 07 Jun 2017, 20:58, edited 1 time in total.
Renamed the topic.
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: Is −2 < z < 2?  [#permalink]

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1
Nathanlambson wrote:
Is −2 < z < 2?

(1) z^2 < 4

(2) z^2 > −4

We need to determine whether −2 < z < 2.

Statement One Alone:

z^2 < 4

Simplifying the inequality in statement one, we have:

√z^2 < √4

z < 2

or

-z < 2

z > -2

Thus, -2 < z < 2, so statement one is sufficient to answer the question.

Statement Two Alone:

z^2 > −4

The information in statement two is not sufficient to answer the question. The square of every real number is non-negative and therefore greater than -4; so, statement two is satisfied by every real number. Thus, z could be any real number. Statement two alone is not sufficient to answer the question.

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BSchool Moderator G
Joined: 15 May 2017
Posts: 212
Re: Is −2 < z < 2?  [#permalink]

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Nathanlambson wrote:
Is −2 < z < 2?

(1) z^2 < 4

(2) z^2 > −4

Statement 1 is sufficient. Any number squared will be positive. If z^2 is less than 4, the absolute value of Z must be less than 2. Therefore - 2<z<2

Statement 2 is insufficient. Z can be any number. For instance, Z=3 or - 3, z^2=9. Alternatively, z =1, z^2 =1. Both satisfy the equation , but don't tell us if Z is in the desired range.

The answer is that only a is sufficient.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1409
Location: India
Re: Is −2 < z < 2?  [#permalink]

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Statement 1. z^2 < 4 implies that: -2 < z < 2
This statement directly answers the question with YES. So Sufficient.

Statement 2. z^2 > -4. All squares are either 0 or positive. So no matter what the value of z,
its square will be > -4. This doesn't answer whether -2 < z < 2 or not. So Insufficient. Re: Is −2 < z < 2?   [#permalink] 08 Jun 2017, 00:01
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# Is −2 < z < 2?  