NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 20:29 It is currently 25 Apr 2024, 20:29
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If n is a positive integer, is n odd?

SORT BY:
Date
Kudos
Tags:
Difficulty: Sub 505 Levelx   Number Propertiesx               
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619043 [9]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If n is a positive integer, is n odd? [#permalink] New post   14 Jul 2014, 03:38
3
Kudos
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

91% (00:42) correct 9% (00:48) wrong based on 950 sessions
Hide Show timer Statistics
If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29934 [5]
Given Kudos: 799
Location: Canada
Send PM
Re: If n is a positive integer, is n odd? [#permalink] New post   13 Dec 2019, 12:43
4
Kudos
1
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:

GMAT weekly questions



If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.


Given: n is a positive integer

Target question: Is n odd?

Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN

#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN


Statement 1: 3n is odd
Since 3 is ODD, we are told that (ODD)(n) = ODD
From Rule #4 above, we can conclude that n is ODD
The answer to the target question is YES, n IS odd
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n + 3 is even
in other words, n + ODD = EVEN
From Rule #1 above, we can conclude that n is ODD
The answer to the target question is YES, n IS odd
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619043 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If n is a positive integer, is n odd? [#permalink] New post   14 Jul 2014, 03:39
1
Kudos
Expert Reply
Bunuel wrote:

GMAT weekly questions



If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.


Statement (1) implies that n is odd, for if n were even, any multiple of n would be even. Therefore, the answer must be A or D.
Statement (2) also implies that n is odd, since 3 less than any even number is an odd number.

Since either (1) or (2), taken separately, is sufficient to answer the question, the best answer is D.
User avatar
S
hemantbafna
Manager
Manager
Joined: 30 Jan 2020
Posts: 167
Own Kudos [?]: 79 [1]
Given Kudos: 528
Location: India
WE:Accounting (Accounting)
Send PM
GMAT ToolKit User
Re: If n is a positive integer, is n odd? [#permalink] New post   12 Aug 2020, 22:38
1
Kudos
Bunuel wrote:

GMAT weekly questions



If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.



(1) If 3n is odd- We know that if we multiply any odd number by an odd number the resultant is a odd number.
Therefore n is odd.

(2) n+3 is even- When we add odd number with an odd number the resultant is an odd number.

Therefore D
User avatar
S
garcmillan
Manager
Manager
Joined: 24 Sep 2015
Posts: 71
Own Kudos [?]: 78 [1]
Given Kudos: 79
Location: Spain
Concentration: Strategy, Entrepreneurship
GPA: 3.9
WE:Management Consulting (Consulting)
Send PM
Re: If n is a positive integer, is n odd? [#permalink] New post   13 Aug 2020, 11:31
1
Kudos
Hi all,

if we didn't know the rules mentioned by BrentGMATPrepNow, we could us the trial and error method:

If n is a positive integer, is n odd?

(1) 3n is odd.

n=2 -> 3n = 6 (EVEN)
n=3 -> 3n = 9 (ODD)
n=4 -> 3n = 12 (EVEN)
n=5 -> 3n = 15 (ODD)

It seems when n is ODD, 3n is odd, so if we are given that 3n is odd, we can say that n is odd for sure

SUFFICIENT

(2) n + 3 is even

n=2 -> n + 3 (ODD)
n=3 -> n + 3 (EVEN)
n=4 -> n + 3 (ODD)
n=5 -> n + 3 (EVEN)

It seems when n is ODD, n + 3 is even, so if we are given that n + 3 is even, we can say that n is odd for sure

SUFFICIENT

ANSWER D
User avatar
danielpincente
Intern
Intern
Joined: 04 Jan 2024
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
If n is a positive integer, is n odd? [#permalink] New post   Updated on: 04 Jan 2024, 23:43
If n is a positive integer, is n odd?

(1) 3n is odd.

(2) n + 3 is even.


Statement (1) implies that n is odd, for if n were even, any multiple of n would be even. Therefore, the answer must be A or D. Statement (2) also implies that n is odd, since 3 more than any even number is an odd number. Either (1) or (2), taken separately, is sufficient to answer the question.

When I test (1) - I tried 3(4) = 12, which is even, therefore it is not odd / not sufficient.
When I test (2) - I tried 4 + 3 = 7, which is odd, therefore it is not odd / not sufficient.

This contradicts the solution and I am extremely confused.

Originally posted by danielpincente on 04 Jan 2024, 19:37.
Last edited by Bunuel on 04 Jan 2024, 23:43, edited 3 times in total.
Formatted the question
User avatar
B
Jennk922
Intern
Intern
Joined: 17 Oct 2023
Posts: 10
Own Kudos [?]: 0 [0]
Given Kudos: 1
Location: United States (CA)
Schools: Berkeley Haas (S)
GPA: 3.24
Send PM
Re: Help please - quant DS question [#permalink] New post   04 Jan 2024, 20:04
Statement 1 says 3n is ODD. 3(4) is even. 3(3) is odd. This statement one is sufficient

Statement 2 says 3+n is EVEN. 3+7= 10 (even. Statement 2 is sufficient.
I think you confused what the results of each statement said.

Posted from my mobile device
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31933 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: Help please - quant DS question [#permalink] New post   04 Jan 2024, 20:29
Expert Reply
danielpincente wrote:
Question:

If n is a positive integer, is n odd?

(1) 3n is odd.

(2) n + 3 is even.

When I test (1) - I tried 3(4) = 12, which is even, therefore it is not odd / not sufficient.
When I test (2) - I tried 4 + 3 = 7, which is odd, therefore it is not odd / not sufficient.

This contradicts the solution and I am extremely confused.


You are testing n as 4 or even, and it gives you the opposite answer. This means n is not even, and should be sufficient.

1) 3n is odd.
3*n = odd. For a product to be odd, both the integer should be odd. This n is odd.
Sufficient

2) n+3 is even.
Sum of two numbers is even when both are even or both are odd. Here one is given as 3, so n should also be odd.
Sufficient

D

What is the contradiction you are finding.
User avatar
L
HarshaBujji
Senior Manager
Senior Manager
Joined: 29 Jun 2020
Posts: 411
Own Kudos [?]: 477 [0]
Given Kudos: 219
Location: India
Send PM
Reviews Badge
Re: If n is a positive integer, is n odd? [#permalink] New post   05 Jan 2024, 07:37
danielpincente wrote:
If n is a positive integer, is n odd?

(1) 3n is odd.

(2) n + 3 is even.


Statement (1) implies that n is odd, for if n were even, any multiple of n would be even. Therefore, the answer must be A or D. Statement (2) also implies that n is odd, since 3 more than any even number is an odd number. Either (1) or (2), taken separately, is sufficient to answer the question.

When I test (1) - I tried 3(4) = 12, which is even, therefore it is not odd / not sufficient.
When I test (2) - I tried 4 + 3 = 7, which is odd, therefore it is not odd / not sufficient.

This contradicts the solution and I am extremely confused.



We know that n is a positive integer

Stmt 1: 3n is odd.
Product of 2 odd numbers is odd, If the product is odd then both the numbers has to be odd.
Hence n is odd.

Statement 1 lone is sufficient.



Stmt 2: n + 3 is even.
o + o = e
e + e = e

Moreover we can consider n+3 = 2k,
So n = 2k - 3
=> n = 2(k-2) + 1
=> n = 2l+1 [If n has to be positive l >0]

Hence n is odd.

Statement 2 alone is also sufficient.

IMO D.
GMAT Club Bot
gmatclubot
Re: If n is a positive integer, is n odd? [#permalink]
05 Jan 2024, 07:37
Moderator:
Bunuel
Math Expert
92915 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions