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Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14

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Bunuel
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Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   25 Oct 2015, 09:13
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Is zp negative?

(1) pz^4 < 0
(2) p + z^4 = 14
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E
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   26 Oct 2015, 06:14
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Bunuel wrote:
Is zp negative?

(1) pz^4 < 0
(2) p + z^4 = 14

Kudos for a correct solution.


Question : Is zp negative?

Statement 1: pz^4 < 0
i.e. p is Negative because z^4 must be positive for given Inequation
But since the sign of z is still unknown hence,
NOT SUFFICIENT

Statement 2: p + z^4 = 14
As per this inequation p and z can have any sign positive or negative hence nothing can be concluded
NOT SUFFICIENT

Combining the two statements
p is Negative but even after combining the two statement we can't conclude the sign of z. Hence,
NOT SUFFICIENT

Answer: Option E
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   03 Aug 2017, 14:12
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Bunuel wrote:
Is zp negative?

(1) pz^4 < 0
(2) p + z^4 = 14

Kudos for a correct solution.


Target question: Is zp negative?

Statement 1: p(z^4) < 0
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of p and z that satisfy statement 1. Here are two:
Case a: p = -1 and z = 1. In this case, pz = (-1)(1) = -1. So, pz IS negative.
Case b: p = -1 and z = -1. In this case, pz = (-1)(-1) = 1. So, pz is NOT negative.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p + (z^4) = 14
There are several values of p and z that satisfy statement 1. Here are two:
Case a: p = -2 and z = 2. In this case, pz = (-2)(2) = -4. So, pz IS negative.
Case b: p = -2 and z = -2. In this case, pz = (-2)(-2) = 4. So, pz is NOT negative.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are still several values of p and z that satisfy BOTH statements. Here are two:
Case a: p = -2 and z = 2. In this case, pz = (-2)(2) = -4. So, pz IS negative.
Case b: p = -2 and z = -2. In this case, pz = (-2)(-2) = 4. So, pz is NOT negative.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:
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E
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   26 Oct 2015, 01:28
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Answer is E

Explaination:- Question asks, Is zp <0 ?

Considering statement (1) pz^4 < 0 , as z has even power we cannot say anything about whether z is + or -. It follows BCE.

Now consider statement (2) p + z^4 = 14, => p=14-z^4, now this leads us to options p can be + or negative based on z's values.
For example, p=14-16 is -2 and p=14-1^4 is 13.

Even combining both of them does not provide any solution so I go for option E.
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   26 Oct 2015, 04:57
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Is zp negative?

(1) pz^4 < 0
(2) p + z^4 = 14

Sol. zp is negative when either z or p is negative
1) pz^4 <0 so z^4 is always +ve sp p is -ve but we dont know anything about z so insufficient
2) p + z^4 = 14 Dont know anything about p and z so insufficient

1) + 2) p(14-p) <0 either p <0 or 14 - p <0 or p >14 so noot sufficient

E must be the correct answer
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   26 Dec 2015, 19:00
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In order for \(zp<0\), only one out of z and p must be negative and not both.

Statement 1 tells that \(p<0\) but nothing about z (as \(z^4\) will always be positive whether z is positive or negative). Hence, insufficient.
Statement 2 doesn't tells anything about the signs of p and z as they could be either positive or negative to get a sum of 14. Hence, insufficient.

Combining both statements, we know that \(p<0\) and \(p+z^4=14\), that only helps us to conclude that \(z^4>14\), which again doesn't helps in confirming the sign of z (i.e. whether it's positive or negative). Hence, insufficient.

Answer: E

Hope it helps.
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   09 Jul 2018, 23:14
Hi,

I don't have a copy of og16,

will someone confirm whether in statement 1. only p is raised to 4 or zp is raised to 4?
it looks ambiguous...i assumed it is only z^4 and got it right
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   09 Jul 2018, 23:45
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ENEM wrote:
Hi,

I don't have a copy of og16,

will someone confirm whether in statement 1. only p is raised to 4 or zp is raised to 4?
it looks ambiguous...i assumed it is only z^4 and got it right


If pz were raised to the power it would be written (pz)^4. Since it's written pz^4, then only z is raised to the power.
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   11 Apr 2021, 18:49
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   12 May 2021, 09:16
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Bunuel wrote:
Is zp negative?

(1) pz^4 < 0
(2) p + z^4 = 14

Kudos for a correct solution.

Solution:

Question Stem Analysis:

We need to determine whether zp < 0. Recall that in order for zp to be negative, one of the values z or p must be positive and the other negative.

Statement One Only:

Since pz^4 < 0, neither p nor z is 0. Since z^4 > 0 regardless whether z is positive or negative, we see that p must be negative in order for pz^4 < 0. However, since z could be either positive or negative, we can’t determine whether zp < 0. Statement one alone is not sufficient.

Statement Two Only:

If z = 1, then p = 13, and zp = 13 is not negative. However, if z = 2, then p = -2, and zp = -4 is negative. Statement two alone is not sufficient.

Statements One and Two Together:

From statement one, we see that p is negative. Now, using statement two and letting p = -2, we’ll have z equal to 2 or -2. If z = 2, then zp = -4 is negative. However, if z = -2, then zp = 4 is not negative. Both statements are not sufficient.

Answer: E
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   23 May 2021, 00:46
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Bunuel wrote:
Is zp negative?

(1) pz^4 < 0
(2) p + z^4 = 14

Kudos for a correct solution.


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Answer: Option E

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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink] New post   19 Jul 2023, 21:52
Is zp negative?

(1) pz^4 < 0
p must be -ve, but we don't know about z. (Insufficient)
(2) p + z^4 = 14
z can be anything, p can be -ve of +ve. (Insufficient)

Using Both again, we don't know about z. Ans E
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Re: Is zp negative? (1) pz^4 < 0 (2) p + z^4 = 14 [#permalink]
19 Jul 2023, 21:52
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