GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 Feb 2020, 01:34 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is zp negative?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61412

### Show Tags

7
35 00:00

Difficulty:   25% (medium)

Question Stats: 74% (01:35) correct 26% (01:26) wrong based on 2141 sessions

### HideShow timer Statistics

Is zp negative?

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

Kudos for a correct solution.

_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3186
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)

### Show Tags

14
5
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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
##### General Discussion
CEO  G
Joined: 20 Mar 2014
Posts: 2538
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)

### Show Tags

1
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.
Manager  Joined: 11 Sep 2013
Posts: 103

### Show Tags

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
Intern  Joined: 02 Jan 2014
Posts: 36

### Show Tags

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.
Manager  Joined: 22 Feb 2015
Posts: 55
Location: United States
Concentration: Finance, Operations
GMAT Date: 04-01-2015
GPA: 3.98

### Show Tags

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
Manager  B
Joined: 12 Feb 2011
Posts: 77

### Show Tags

2
1
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.
Intern  B
Joined: 18 Jan 2017
Posts: 31

### Show Tags

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.
Manager  S
Joined: 05 Dec 2016
Posts: 230
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29 ### Show Tags

Playing around with different signs of z we get different signs of pz, thus E.
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4345

### Show Tags

2
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

_________________
Senior Manager  P
Joined: 15 Nov 2016
Posts: 267

### Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 61412

### Show Tags

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.
_________________
VP  D
Joined: 09 Mar 2016
Posts: 1221

### Show Tags

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? IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1388
Location: India
WE: Engineering (Other)

### Show Tags

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.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Math Expert V
Joined: 02 Sep 2009
Posts: 61412

### Show Tags

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: $$\sqrt{11}$$ or $$-\sqrt{11}$$
_________________
Manager  B
Joined: 03 Aug 2017
Posts: 102

### Show Tags

Bunuel wrote:
Is zp negative?

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

Kudos for a correct solution.

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.

Originally posted by mimajit on 29 Sep 2019, 03:19.
Last edited by mimajit on 13 Oct 2019, 21:41, edited 1 time in total.
Manager  B
Joined: 03 Aug 2017
Posts: 102

### Show Tags

Bunuel wrote:
Is zp negative?

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

Kudos for a correct solution.

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.

Intern  B
Joined: 23 Nov 2018
Posts: 28

### Show Tags

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.

Bunuel wrote:
Is zp negative?

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

Kudos for a correct solution.

Posted from my mobile device
Intern  B
Joined: 28 Jan 2019
Posts: 39
GMAT 1: 730 Q47 V42

### Show Tags

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. Re: Is zp negative?   [#permalink] 13 Nov 2019, 07:11
Display posts from previous: Sort by

# Is zp negative?  