GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 05 Dec 2019, 10:55

### 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

# Is n negative?

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Up again.
Joined: 31 Oct 2010
Posts: 458
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42

### Show Tags

19 Apr 2011, 05:54
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:58) correct 40% (02:00) wrong based on 93 sessions

### HideShow timer Statistics

Is n negative?

(1) n^5(1 - n^4) < 0
(2) n^4 - 1 < 0

_________________
My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html
Retired Moderator
Joined: 16 Nov 2010
Posts: 1232
Location: United States (IN)
Concentration: Strategy, Technology

### Show Tags

19 Apr 2011, 06:35
(1)
n^5 (1-n^4) < 0

So either n^5 < 0 and (1-n^4) > 0

Or n^5 > 0 and 1 - n^4 < 0

So insufficient (n^4 is always > 0)

(2)

n^4 - 1 < 0

But we're not sure about sign of n

(1) and (2) say :

n^5 < 0, so n < 0

_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Retired Moderator
Joined: 20 Dec 2010
Posts: 1547

### Show Tags

19 Apr 2011, 08:30
1
gmatpapa wrote:
Is n negative?

1. $$n^5$$$$(1-n^4)$$ $$< 0$$
2. $$n^4-1 < 0$$

Is $$n<0$$

1. $$n^5(1-n^4)< 0$$

$$n^5(n^4-1)> 0$$
is similar to saying:
$$n(n^2-1)>0$$
$$(n-1)n(n+1)>0$$

Three roots: -1, 0, 1.

The above expression would be true for;
$$n>1 \hspace{2} OR \hspace{2} -1<n<0$$
Not Sufficient.

2. $$n^4-1 < 0$$

Similar to:
$$n^2-1<0$$
$$(n+1)(n-1)<0$$

Two roots: -1,1.
The above expression would be true for;
$$-1<n<1$$
Not Sufficient.

Combining both;
$$-1<n<0$$
Sufficient.

Ans: "C"
Intern
Joined: 07 Jun 2011
Posts: 35

### Show Tags

22 Aug 2011, 21:59

Statemet 1: to get a negative result we must have one of the two variables < 0 and the other > 0

in our case n^5 < 0 and 1-n^4 > 0 gives a negative result.

the same out come is arrrived at when n^5 is > 0 and 1 - n^4 is < 0 so not sifficient

statment 2 is also not sifficient; n could be - 2 or + 2

combining we will get the result
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9848
Location: Pune, India

### Show Tags

22 Aug 2011, 23:03
shashankp27 wrote:
Is n negative?
1. n^5(1 – n^4) < 0
2. n^4 – 1 < 0

Go step by step.

Question: Is n negative?

Statement 1: $$n^5(1 - n^4) < 0$$
Re-write as: $$n^5(n^4 - 1) > 0$$ (I do this only for convenience. It is easier to handle >0 because either both are positive or both negative so less confusion.)
This tells me that either both $$n^5$$ and $$(n^4 - 1)$$ are positive (which means n is positive) or both are negative (which means n is negative). n can be positive or negative so not sufficient.

Statement 2: $$n^4 - 1 < 0$$
This implies that n is between -1 and 1.

How?
$$n^4 - 1 = (n^2 + 1)(n^2 - 1) = (n^2 + 1)(n + 1)(n - 1)$$
$$n^2 + 1$$ is always positive so we can ignore it.
We get, $$(n+1)(n - 1) < 0$$
-1 < n < 1 (check out: inequalities-trick-91482.html#p804990)

Since n can be positive or negative, not sufficient alone.

Using both statements together,
$$n^4 - 1$$ is negative, so from the analysis of statement 1, $$n^5$$ must be negative too. This means n must be negative. Sufficient.
_________________
Karishma
Veritas Prep GMAT Instructor

Current Student
Joined: 08 Jan 2009
Posts: 285
GMAT 1: 770 Q50 V46

### Show Tags

23 Aug 2011, 00:06
is n < 0?

1) n^5(1 – n^4) < 0
n^5 - n^9 < 0
n^5 < n^9
n < n^5

n > 1 or -1 < n < 0. NS.

2) n^4 - 1 < 0

-1 < n < 1. NS.

1+2)
n > 1 or -1 < n < 0.
n < 1, therefore, -1 < n < 0

C.
Manager
Joined: 09 Feb 2011
Posts: 197
Concentration: General Management, Social Entrepreneurship
Schools: HBS '14 (A)
GMAT 1: 770 Q50 V47

### Show Tags

23 Aug 2011, 00:35
1. n^5 (1- n^4) <0
for product of two numbers to be negative, they ahve to have different signs.
If n^ 5 is -ve, (1- n^4) has to be +. that is n has to be a negatve number, and also n has to be a fraction (only then (1- n^4) will be positive. Thus this gives n is a negative, proper fraction
If n^5 is +, (1- n^4) has to be negative. n has to be positive (for n^5 to be positive) , and n has to be a number greaters than - for (1- n^4) to be negative - any valuse less than 1 will always give (1- n^4) as +.
Thus from one n can be a positive number more than 1 or a negative fraction. Insufficient to say whether n is negative or not

2. (n^4 - 1) < 0
(n^4 - 1) is negative that means n^ 4 is less than 1, can be true for both negative and positive fratcions. thus not sufficient.

Together: if (n^4 - 1) < 0, (1- n^4) > 0. From 1, n^5 (1- n^4) <0
That means n^5 has to be negative (only then the product can be negative)
for n ^5 to be negative, n has to be negative
Hence Both togetehr are sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 59561

### Show Tags

24 Jun 2013, 01:30
1
Is n negative?

(1) n^5(1 - n^4) < 0. For convenience rewrite this as $$n^5(n^4-1) > 0$$ --> n can be positive as well as negative: consider n=2 and n=-1/2. Not sufficient.

(2) n^4 - 1 < 0 --> $$n^4<1$$ --> $$-1<n<1$$. Not sufficient.

(1)+(2) Since from (2) $$n^4 - 1 < 0$$, then from (1) $$n^5$$ must also be negative (in order n^5(n^4-1) to be positive). $$n^5<0$$ means that n is negative. Sufficient.

Hope it's clear.
Non-Human User
Joined: 09 Sep 2013
Posts: 13709

### Show Tags

20 Feb 2019, 20:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is n negative?   [#permalink] 20 Feb 2019, 20:10
Display posts from previous: Sort by