BTGmoderatorDC wrote: ↑Sun Jan 26, 2020 9:58 pm
If an ≠ 0 and n is a positive integer, is n odd?
(1) a^n + a^(n + 1) < 0
(2) a is an integer.
OA
C
Source: Manhattan Prep
Given: an ≠ 0 and n is a positive integer;
Since an ≠ 0, we have a ≠ 0.
We have to ascertain whether is n odd.
Let's take each statement one by one.
(1) a^n + a^(n + 1) < 0
a^n + a^n*a < 0
a^n*(1 + a) < 0
=> the product of a^n and (1 + a) is negative. It is possible in two cases: one of them is positive and the other is negative.
Case 1: Say a^n < 0 and (1 + a) > 0
Given that 1 + a > 0, we have a > –1. Since a^n is negative, a must be negative and n must be odd. Thus, we have 0 < a < –1.
Case 2: Say a^n > 0 and (1 + a) < 0
Given that 1 + a < 0, we have a < –1. Since a^n is positive, and a is negative, we must have n even.
No unique value of n. Insufficient.
(2) a is an integer.
Certainly insufficient.
(1) and (2) together
In view of Statement 2, Case 1 discussed in Statement 1 is invalid; thus, as per Case 2, n is even. The answer is no: a unique answer. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
_________________
Manhattan Review
Locations:
Manhattan Review Jayanagar |
GMAT Prep Jayanagar |
GRE Prep Madhapur |
Kukatpally GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
