If n is an integer, which of the following must be even?
A) n + 1
B) n + 2
C) 2n
D) 2n + 1
E) n^2
OA: C
If n is an integer, which
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 93
- Joined: Mon Apr 25, 2016 2:22 pm
- Thanked: 1 times
- Followed by:1 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
The definition of an even number is that it can be written as the product of 2 and some integer.boomgoesthegmat wrote:If n is an integer, which of the following must be even?
A) n + 1
B) n + 2
C) 2n
D) 2n + 1
E) n^2
So the correct answer is C
Alternatively, we can show that A, B, D and E need not be even numbers.
A) If n = 2, then n+1 is NOT even. ELIMINATE.
B) If n = 1, then n+2 is NOT even. ELIMINATE.
C) If n = 1, then 2n+1 is NOT even. ELIMINATE.
D) If n = 1, then n^2 is NOT even. ELIMINATE.
Cheers,
Brent
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Since an the product of an even number and any integer is even, 2n will always be even.boomgoesthegmat wrote:If n is an integer, which of the following must be even?
A) n + 1
B) n + 2
C) 2n
D) 2n + 1
E) n^2
Answer: C
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
We're told that N is an INTEGER. We're asked which of the following MUST be even (which really means "which of the following is ALWAYS EVEN no matter how many different examples we can come up with?"). This question can be solved in a couple of different ways. There are a number of different Number Property rules involved in this prompt, so we can do a quick review of all of them and find the correct answer that way.
Answer A: N+1.... adding 1 to an EVEN leads to an ODD, adding 1 to an ODD leads to an EVEN. Eliminate Answer A.
Answer B: N+2.... adding 2 to an EVEN leads to an EVEN, adding 2 to an ODD leads to an ODD. Eliminate Answer B.
Answer C: 2N.... multiplying ANY integer by 2 leads to an EVEN. This is ALWAYS EVEN.
Answer D: 2N+1.... multiplying ANY integer by 2 leads to an EVEN and then adding 1 leads to an ODD.
Answer E: N^2.... squaring an EVEN leads to an EVEN, squaring an ODD leads to an ODD.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that N is an INTEGER. We're asked which of the following MUST be even (which really means "which of the following is ALWAYS EVEN no matter how many different examples we can come up with?"). This question can be solved in a couple of different ways. There are a number of different Number Property rules involved in this prompt, so we can do a quick review of all of them and find the correct answer that way.
Answer A: N+1.... adding 1 to an EVEN leads to an ODD, adding 1 to an ODD leads to an EVEN. Eliminate Answer A.
Answer B: N+2.... adding 2 to an EVEN leads to an EVEN, adding 2 to an ODD leads to an ODD. Eliminate Answer B.
Answer C: 2N.... multiplying ANY integer by 2 leads to an EVEN. This is ALWAYS EVEN.
Answer D: 2N+1.... multiplying ANY integer by 2 leads to an EVEN and then adding 1 leads to an ODD.
Answer E: N^2.... squaring an EVEN leads to an EVEN, squaring an ODD leads to an ODD.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich