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

 It is currently 16 Oct 2019, 12:59

### 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

# If a^n ≠ 0 and n is a positive integer, is n odd?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 10 Sep 2013
Posts: 22
Location: India
Concentration: Accounting, Finance
GMAT Date: 10-25-2013
GPA: 3.66
If a^n ≠ 0 and n is a positive integer, is n odd?  [#permalink]

### Show Tags

Updated on: 20 Oct 2013, 04:43
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:30) correct 33% (01:55) wrong based on 131 sessions

### HideShow timer Statistics

If a^n ≠ 0 and n is a positive integer, is n odd?

(1) a^n + a^(n+1) < 0

(2) a is an integer.

_________________
Strive for Excellence....!!!!!

Originally posted by jellybean23 on 19 Oct 2013, 12:14.
Last edited by Bunuel on 20 Oct 2013, 04:43, edited 1 time in total.
Edited the question and added the OA.
Manager
Joined: 08 Dec 2012
Posts: 61
Location: United Kingdom
WE: Engineering (Consulting)
Re: If a^n ≠ 0 and n is a positive integer, is n odd?  [#permalink]

### Show Tags

19 Oct 2013, 13:42
1
1
Statement 1:

This essentially says $$a$$ is negative and thereby one of the terms $$a^n$$ or $$a^n^+^1$$ is negative (both can't be negative as either $$n$$ is even or $$n+1$$ is even)

Let's assign $$a=-2$$. So $$a^n + a^n^+^1 < 0$$ only when $$n$$ is even. But what happens if $$a$$ is not an integer? Assign $$a=-0.1$$, then for the equation to be less than zero, $$n$$ has to be odd. INSUFFICIENT

Statement 2:

This tells us that $$a$$ is an integer, but does not say anything about $$n$$. INSUFFICIENT

Statement 1 & 2: as discussed under Statement 1, when $$a$$ is a negative integer, $$n$$ has to be even for the equation to be less than zero. So we know $$n$$ is not odd. SUFFICIENT

Intern
Joined: 10 Sep 2013
Posts: 31
Location: United States
Concentration: Strategy, Operations
GMAT Date: 12-10-2013
GPA: 3.5
WE: Operations (Manufacturing)
Re: If a^n ≠ 0 and n is a positive integer, is n odd?  [#permalink]

### Show Tags

19 Oct 2013, 20:11
2
n >0
Statement 1 :
a^n + a^(n+1) < 0
lets put n =1 (odd) , a+a^2 <0 .................. , that means 0 > a > -1,
lets put n=2 (even) , a^2 + a^3 < 0 ........... , that means a < 0

Statement 2 :
a is an integer , but no conclusion about n... insufficient...

Taking both statements together....
only n=2 valid .... which gives n is not an odd no..
Intern
Joined: 10 Sep 2013
Posts: 22
Location: India
Concentration: Accounting, Finance
GMAT Date: 10-25-2013
GPA: 3.66
Re: If a^n ≠ 0 and n is a positive integer, is n odd?  [#permalink]

### Show Tags

19 Oct 2013, 21:50
+1 Kudos !!!!
great explanation by both of you.
Thanks
_________________
Strive for Excellence....!!!!!
Math Expert
Joined: 02 Sep 2009
Posts: 58381
Re: If a^n ≠ 0 and n is a positive integer, is n odd?  [#permalink]

### Show Tags

20 Oct 2013, 04:54
If a^n ≠ 0 and n is a positive integer, is n odd?

a^n ≠ 0 and n is a positive integer implies that a ≠ 0.

(1) a^n + a^(n+1) < 0 --> $$(a+1)a^n<0$$. Two cases:

$$a+1>0$$ and $$a^n<0$$. From first inequality we have that $$a>-1$$. If a is a negative number (say -1/2), then $$(negative)^n$$ to be negative n must be odd.

$$a+1<0$$ and $$a^n>0$$. From first inequality we have that $$a<-1$$, so a is a negative number. Now, $$(negative)^n$$ to be positive n must be even.

Not sufficient.

(2) a is an integer. Clearly insufficient.

(1)+(2) Consider the same two cases but now take into account that a is an integer:

$$a+1>0$$ and $$a^n<0$$. From first inequality we have that $$a>-1$$. Since we know that $$a\neq{0}$$, then a must be a positive integer (1, 2, 3, ...). Next, $$(positive)^n$$ cannot be negative, thus this case is out.

$$a+1<0$$ and $$a^n>0$$. From first inequality we have that $$a<-1$$, so a is a negative integer. Now, $$(negative)^n$$ to be positive n must be even.

Sufficient.

Hope it's clear.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13210
Re: If a^n ≠ 0 and n is a positive integer, is n odd?  [#permalink]

### Show Tags

30 Mar 2018, 23:37
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: If a^n ≠ 0 and n is a positive integer, is n odd?   [#permalink] 30 Mar 2018, 23:37
Display posts from previous: Sort by