Is n negative?

Question

Is n negative?

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

subhashghosh · Answer

(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

fluke · Answer

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

manishgeorge · Answer

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

KarishmaB · Answer

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

pike · Answer

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.

vivesomnium · Answer

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

Bunuel · Answer

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

bumpbot · Answer

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Is n negative?

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