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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(1) pz^4 < 0
=> p<0 but we do not know the sign of z
=> Do not know the sign of pz
=> Insufficient
(2) p + z^4 = 14
We do not know the sign of both p and z
=> Insufficient
(1) + (2): insufficient

Ans: E

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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The main issue is that even with both the statements, we still don't know the sign of "z". It can be either positive or negative. Hence, we cannot say for sure whether zp <0.

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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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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