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Is n negative?

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Is n negative?  [#permalink]

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New post 19 Apr 2011, 05:54
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Is n negative?

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

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Re: Inequalities DS  [#permalink]

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New post 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

Answer - C
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Re: Inequalities DS  [#permalink]

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New post 19 Apr 2011, 08:30
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"
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Re: Is n negative?  [#permalink]

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New post 22 Aug 2011, 21:59
Answer C

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
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Re: Is n negative?  [#permalink]

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New post 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.
Answer C
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Re: Is n negative?  [#permalink]

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New post 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.
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Re: Is n negative?  [#permalink]

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New post 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.
Answer C
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Re: Is n negative?  [#permalink]

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New post 24 Jun 2013, 01:30
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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.

Answer: C.

Hope it's clear.
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Re: Is n negative?  [#permalink]

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