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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zp<0 ?

Per statement 1, pz^4<0 ---> not sufficient, p=-1, z=4 or p=-1, z=-4.

Per statement 2, p + z^4 = 14 ---> p=13, z=-1 gives you a "yes" but p=3, z^4 = 11, not sufficient,

Combining, you still can not eliminate the cases raised above, making E the correct answer.
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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

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.

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

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.

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.

Playing around with different signs of z we get different signs of pz, thus E.

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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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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how is it possible that z^4 = 11 ? what number Z must be n this case?

dave13

Here are my two cents.

The question stem asks: Is either of z or p is negative
But here is the catch, even if you know exact sign of p,
unless you know the exact sign of z, one cannot decide
whether final product will be positive or negative.

If p is negative,
a. but z is negative: final product is positive
b. but z is positive: final product is negative.

St 1 : p\(z^4\)is negative.
Any number raised to even power will always be positive.
But are you sure about sign of that number?

\(1^4\) = 1
\((-1)^4\) = 1

Hence z can be 1 or -1. Insuff
All we know from this statement is that p is negative since\(z^4\) will always be positive.

Coming to St 2:
p + \(z^4\) = 14
Take simple values as below:
13 + \((1)^4\) = 14
13 + \((-1)^4\) = 14
p is positive, z can be positive or negative

You can also take (with same analogy)
-2 + \((2)^4\) = 14
-2 + \((-2)^4\)= 14
p is negative, z can be positive or negative

Combining both statements, I am still not sure about sign of z.
Bottom line: z raised to even power is the culprit or trap here.

Hope this helps.
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A number the fourth power of which equal to 11: \(\sqrt[4]{11}\) or \(-\sqrt[4]{11}\)
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This is how i solved ...

Statement 1: pz^4<0
Case1: p=+ve---even if z is +ve or z is-ve, this will never satisfy the statement pz^4>0 as the result will always be +ve

Case2: p=-ve ----- if z is+ve or -ve answer will always be -ve
so we can not say for sure that z is +ve or -ve

hence we can not determine pz <0 or not.

Statement 2: p+z^4 = 14
as we already know Z^4 will always be +ve but z can be both +ve as well as -ve
and value of p can not be determined

hence we can not determine pz <0 or not.

so the Answer is E

This is how i solved ...

Statement 1: pz^4<0

Sinec we know Z^4 will be a positive no ... as Exponent is an even no ... Also if pz^4<0 and we already know Z^4 is positive means = p=-ve .
But Z can both be positive or neagative, Since we cant determine the sign of Z . Thiis statment is insufficient.

hence we can not determine pz <0 or not.

Statement 2: p+z^4 = 14
as we already know Z^4 will always be +ve but z can be both +ve as well as -ve
and value of p can not be determined

hence we can not determine pz <0 or not.

Both Statements combined we know P is negative but we still donot know the sign of Z hence the ans cant be determined.

so the Answer is E

Did you choose C too and can prove that zp is negative when both are used?

I made a small table that could prove that zp is negative but I had missed one tiny part. Have a look below to find your mistake too

Don't have enough kudos to add an image, so I'll try to condense it this way:-


Eq 1)
says pz^4 < 0
Cases possible:

•Z is -
P is -

•Z is +
P is -


Eq 2)
Says that p+z^4=14

Cases possible-
•Z is +
P is +

•Z is -
P is +

•Z is +
P is -

•Z is -
P is -

Basically, all combinations are possible.

Combining 1) and 2) we have 2 cases remaining.
• Z and P are both negative, and one where
• Z is + and P is -

Hence, zp can be + or -. We can't pick (C)


Kudos is appreciated. Thanks.




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Z*P is negative when either Z or P is negative, but not both. 


1) P*Z^4 < 0 
From this we know z can be either positive or negative, because any integer to an even power is positive. We learn from this that P must be negative. Overall statement 1 is insufficient because if P and Z are negative, the solution will be positive, but if Z is positive then the answer will be negative.

2) P + Z^4 = 14
. From this we know that z can be either positive or negative. We also learn that P can be either positive or negative. Take the example where z=2; we have 2^4 or P+16=14. P=-2. Also insufficient.

Combined, we have:
statement 1: z = +/- p= -
statement 2: z=+/- p = +/-

So we know P is negative, but we still do not know if z is negative or positive, so cannot say definitively whether z*p is positive or negative.