If n is a positive integer, is n divisible by 2?
A)7n-8 is divisible by 20.
B)3n^2+2n+5 is a prime number.
OA: D
If n is a positive integer,is n divisible by 2?
This topic has expert replies
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
We are given that n is a positive integer.NandishSS wrote:If n is a positive integer, is n divisible by 2?
A)7n-8 is divisible by 20.
B)3n^2+2n+5 is a prime number.
OA: D
We have to find out whether n is divisible by 2.
Let's take each statement one by one.
1) 7n - 8 is divisible by 20.
Since 7n - 8 is divisible by 20 (an even number), 7n - 8 must be even.
=> 7n - 8 = Even
7n = Even + 8 = Even
7*n = even
Since 7 is odd, n must be even. Thus, n divisible by 2. Sufficient.
2) 3n^2 + 2n + 5 is a prime number.
3n^2 + 2n + 5 = Odd; it cannot be 2 since 3n^2 + 2n + 5 must be greater than 5 and all the prime numbers greater than 5 are odd.
=> 3n^2 + 2n = Odd - 5
3n^2 + 2n = Odd - Odd
3n^2 + 2n = Even
3n^2 = Even - 2n
3n^2 = Even - Even
3n^2 = Even
Since 3 is odd, n^2 must be even, thereby n must be even. Thus, n divisible by 2. Sufficient.
The correct answer: D
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: Jayanagar | Dilsukhnagar | Himayatnagar | Visakhapatnam | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Hello NandishSS.
I will try to solve your question.
We know that n is a positive integer and we want to know if n is divisible by 2.
First Statement
Hence, this statement is SUFFICIENT.
Second Statement
- Since n is a positive integer then n>0 (n >= 1)
- If n>0 then 3n^2+2n+5>= 10.
- Since 3n^2+2n+5 is a prime number and it is greater or equal than 10, then 3n^2+2n+5 must be an odd number.
So, we have the following: $$3n^2+2n+5=odd\ \ \ \Rightarrow\ \ 3n^2+2n=odd-5\ \ \ \Rightarrow\ \ \ 3n^2+2n=even.$$ $$\Rightarrow\ \ 3n^2=even\ -\ 2n\ \ \ \ \Rightarrow\ \ \ 3n^2=even\ -even\ \ \ \Rightarrow\ \ \ 3n^2=even.$$ Since 3 is odd, then we have to n^2 must be even. This only happens when n is even.
Therefore, n is even and this implies that n is divisible by 2.
So, this statement is also SUFFICIENT.
In conclusion, each statement is SUFFICIENT, so the correct answer is the option D.
I hope it helps.
Regards.
I will try to solve your question.
We know that n is a positive integer and we want to know if n is divisible by 2.
First Statement
This statement tells us that $$7n-8=20\cdot k\ \ \ ,\ \ \ k\in\mathbb{Z}$$ $$\Rightarrow\ \ 7n=20\cdot k\ +8\ \ ,\ \ \ k\in\mathbb{Z}$$ $$\Rightarrow\ \ 7n=2\left(10\cdot k\ +4\right)\ \ ,\ \ \ k\in\mathbb{Z}$$ The last equation says that 7b is divisible by 2 and since 7 is not divisible by 2, we conclude that n is divisible by 2.A)7n-8 is divisible by 20.
Hence, this statement is SUFFICIENT.
Second Statement
Here we have to see the following:B)3n^2+2n+5 is a prime number.
- Since n is a positive integer then n>0 (n >= 1)
- If n>0 then 3n^2+2n+5>= 10.
- Since 3n^2+2n+5 is a prime number and it is greater or equal than 10, then 3n^2+2n+5 must be an odd number.
So, we have the following: $$3n^2+2n+5=odd\ \ \ \Rightarrow\ \ 3n^2+2n=odd-5\ \ \ \Rightarrow\ \ \ 3n^2+2n=even.$$ $$\Rightarrow\ \ 3n^2=even\ -\ 2n\ \ \ \ \Rightarrow\ \ \ 3n^2=even\ -even\ \ \ \Rightarrow\ \ \ 3n^2=even.$$ Since 3 is odd, then we have to n^2 must be even. This only happens when n is even.
Therefore, n is even and this implies that n is divisible by 2.
So, this statement is also SUFFICIENT.
In conclusion, each statement is SUFFICIENT, so the correct answer is the option D.
I hope it helps.
Regards.
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
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
In order for an integer n to be divisible by 2, n must be even. So we need to determine whether n is even.NandishSS wrote:If n is a positive integer, is n divisible by 2?
A)7n-8 is divisible by 20.
B)3n^2+2n+5 is a prime number.
Statement One Alone:
7n-8 is divisible by 20.
That is, 7n - 8 = 20k for some integer k. So we have:
7n = 20k + 8
n = 4(5k + 2)/7
Since n is an integer and 4 and 7 have no common factor other than 1, then 5k + 2 must be divisible by 7. In other words, (5k + 2)/7 is an integer.
Thus, we see that 4(5k + 2)/7 is the same as 4 x integer, which will always be even, so n will always be even. Statement one alone is sufficient to answer the question.
Statement Two Alone:
3n^2+2n+5 is a prime number.
Notice that since n is a positive integer, 3n^2+2n+5 must be greater than 2.
If 3n^2 + 2n + 5 is a prime, then it must be an odd prime and the only way 3n^2+2n+5 is an odd prime is if n is even. Statement two alone is also sufficient to answer the question.
Answer: D
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