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.
Veritas Prep | GMAT Instructor
Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews