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Is zp negative?

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Is zp negative?  [#permalink]

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25 Oct 2015, 09:13
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Question Stats:

73% (01:35) correct 27% (01:25) wrong based on 1991 sessions

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Is zp negative?

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

Kudos for a correct solution.

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Re: Is zp negative?  [#permalink]

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26 Oct 2015, 06:14
10
4
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

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Re: Is zp negative?  [#permalink]

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25 Oct 2015, 09:47
Bunuel wrote:
Is zp negative?

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

Kudos for a correct solution.

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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Re: Is zp negative?  [#permalink]

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25 Oct 2015, 09:49
2
Bunuel wrote:
Is zp negative?

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

Kudos for a correct solution.

(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
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Re: Is zp negative?  [#permalink]

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26 Oct 2015, 01:28
2
1

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?  [#permalink]

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26 Oct 2015, 04:57
4
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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Is zp negative?  [#permalink]

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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.

Hope it helps.
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Re: Is zp negative?  [#permalink]

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21 Jan 2017, 10:27
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.
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Re: Is zp negative?  [#permalink]

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16 Feb 2017, 04:00
Playing around with different signs of z we get different signs of pz, thus E.
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Re: Is zp negative?  [#permalink]

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03 Aug 2017, 14:12
1
Top Contributor
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

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Re: Is zp negative?  [#permalink]

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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?  [#permalink]

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09 Jul 2018, 23:45
1
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?  [#permalink]

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16 Aug 2018, 03:38
ENGRTOMBA2018 wrote:
Bunuel wrote:
Is zp negative?

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

Kudos for a correct solution.

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.

how is it possible that z^4 = 11 ? what number Z must be n this case?
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Is zp negative?  [#permalink]

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16 Aug 2018, 06:08
1
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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Is zp negative?  [#permalink]

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16 Aug 2018, 06:26
1
dave13 wrote:
ENGRTOMBA2018 wrote:
Bunuel wrote:
Is zp negative?

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

Kudos for a correct solution.

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.

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

A number the fourth power of which equal to 11: $$\sqrt[4]{11}$$ or $$-\sqrt[4]{11}$$
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Is zp negative?   [#permalink] 16 Aug 2018, 06:26
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