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What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0

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What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   19 Mar 2019, 05:17
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What is the range of values for \(x^2\) given that \((x^2 + 4)(x^2 - 2) < 0\) ?


(A) \(-4 < x^2 < 2\)

(B) \(0 ≤ x^2 ≤ 2\)

(C) \(0 ≤ x^2 < 2\)

(D) \(0 < x^2 < 2\)

(E) \(-∞ < x < 2\)
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C
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   26 Mar 2019, 10:17
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   26 Mar 2019, 23:28
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


can you explain why A is wrong? the values in this range satisfy the condition
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   26 Mar 2019, 23:32
Ish1996 wrote:
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


can you explain why A is wrong? the values in this range satisfy the condition


the range option A does not satisfy the inequality...
see we need a range where we get values<0 ; so substitute different values and you shall get the answer.
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Ish1996
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   26 Mar 2019, 23:50
Ish1996 wrote:
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


can you explain why A is wrong? the values in this range satisfy the condition


Yeah you are right, I forgot about -2, thanks
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   30 Mar 2019, 10:30
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


In the equation (x^2 + 4)(x^2-2)<0..either (X^2 + 4) is negative or (x^2 - 2) is negative.

Clearly X^2+4 can never be negative. So X^2-2 is negative

X^2-2<0

x^2<2...only option C seems to agree with the equation
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   30 Mar 2019, 11:33
Given, (x^2+4)(x^2-2)<0

So, in between (x^2+4) and (x^2-2), one expression must be positive and the other one must be negative.

Since x^2=a square value=always Non negative, (x^2+4) must be positive and (x^2-2) must be negative.

Thus, (x^2-2)<0
Or, x^2<2
So, x^2 must be less then 2 and since x^2 is a square value, it must be NON negative.

X^2 must be 0 or greater than 0 but less than 2.

My answer is C.

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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   18 Oct 2021, 10:26
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


What about imaginary numbers? Do I need to forget about this concept on the GMAT? Because X could take values of 3i, 2i, etc. and therefore X^2 would be -3, -2, etc.
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   18 Oct 2021, 10:32
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HermesM11 wrote:
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


What about imaginary numbers? Do I need to forget about this concept on the GMAT? Because X could take values of 3i, 2i, etc. and therefore X^2 would be -3, -2, etc.


All numbers on the GMAT are real numbers by default.
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   18 Oct 2021, 22:06
EncounterGMAT wrote:
What is the range of values for \(x^2\) given that \((x^2 + 4)(x^2 - 2) < 0\) ?


(A) \(-4 < x^2 < 2\)

(B) \(0 ≤ x^2 ≤ 2\)

(C) \(0 ≤ x^2 < 2\)

(D) \(0 < x^2 < 2\)

(E) \(-∞ < x < 2\)



Let x^2= P

(P+4)(P-2)<0

So -4<P<2

as X^2 can not be negative so -4 is discarded.
0<=P<2
Because 0 is one of the solution included in the range of P.
So answer is 0≤ x^2 < 2
C.
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   20 Oct 2021, 13:28
How to solve through wavy line method?
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink] New post   05 Jul 2023, 09:35
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Re: What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 [#permalink]
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