What is the value of the integer n? (1) n(n + 2) = 15 (2) (n + 2)^n = 125
OA is C
Can't match upto OA
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 172
- Joined: Fri Oct 21, 2011 9:10 pm
- Thanked: 7 times
- Followed by:2 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: What is the value of the integer n?satishchandra wrote:What is the value of the integer n?
(1) n(n + 2) = 15
(2) (n + 2)^n = 125
OA is C
Statement 1: n(n + 2) = 15
Expand: n^2 + 2n = 15
Set equal to zero: n^2 + 2n - 15 = 0
Factor: (n+5)(n-3) = 0
So, n = -5 or 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: (n + 2)^n = 125
Well, the question tells us that n is an integer. So, this certainly limits our options.
First recognize that 125 = (5)(5)(5)
Also recognize that if n is an integer, then n+2 must be an integer.
Consider this related question. If n and x are both integers, what are some possible solutions to x^n = 125?
I can see only two case:
case a: 125^1, that is x=125 and n=1
case b: 5^3, that is x=5 and n=3
Case a doesn't work for the given equation: (n + 2)^n = 125
If n=1, then we get (1 + 2)^1 = 3
Case b does work for the given equation: (n + 2)^n = 125
If n=3, then we get (3 + 2)^2 = 125
So, statement 2 suggests that n must equal 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
UNLESS I'M TOTALLY MISSING SOMETHING
Cheers,
Brent
- anuprajan5
- Master | Next Rank: 500 Posts
- Posts: 279
- Joined: Mon Jun 25, 2012 10:56 pm
- Thanked: 60 times
- Followed by:10 members
Thank you. I racked my head over how this could be C
Regards
Anup
The only lines that matter - are the ones you make!
https://www.youtube.com/watch?v=kk4sZcG ... ata_player
Anup
The only lines that matter - are the ones you make!
https://www.youtube.com/watch?v=kk4sZcG ... ata_player