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555-605 Level|   Exponents|   Inequalities|   Number Properties|                           
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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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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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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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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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ENEM
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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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Bunuel
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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Bunuel
Is zp negative?

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

Answer: Option E

Video solution by GMATinsight

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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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