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

 It is currently 15 Oct 2019, 20:27

### 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 {n} denote the remainder when 3n is divided by 2 then

Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Sep 2009
Posts: 16
If {n} denote the remainder when 3n is divided by 2 then  [#permalink]

### Show Tags

29 Sep 2009, 02:44
4
19
00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:58) correct 35% (02:14) wrong based on 204 sessions

### HideShow timer Statistics

If {n} denote the remainder when 3n is divided by 2 then which of the following is equal to 1 for all positive integers n?

I. {2n+1}
II. {2n}+1
III. 2{n+1}

A. I only
B. II only
C. I and II
D. III only
E. II and III
Senior Manager
Joined: 30 Nov 2008
Posts: 421
Schools: Fuqua

### Show Tags

29 Oct 2009, 17:20
3
2
This is another way of solving the problem.

It is given that when 3n is divided by 2, the remainder is denoted by {n}. for all positive integers of n. This mean, {n} can be either 0 or 1 depending on whether n is even or odd. Now we need to find which of the following remainders result in 1.

This is like saying if f(n) is the remainder when 3n/2, then what values of the function results in 1.

1. {2n+1} is the remainder obtained when 3(2n+1) is divided by 2. ==> Obviously this results in 1.
2. {2n}+1 can be treated as the remainder obtained when 3(2n) is divided by 2 + adding 1 ==> Obviously this results in 1.
3. 2{n+1} can be obtained when 2 * 3(n+1) is divided by 2. This results in 0.

Hence my take will be C.
##### General Discussion
Senior Manager
Joined: 23 Jun 2009
Posts: 296
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

### Show Tags

29 Sep 2009, 03:42
1
{n}=3n mod 2.

options
1) {2n+1)=6n+3 mod 2 that is always equal 1.
2) {2n}+1= 6n mod 2 + 1 that is always equal 1.
3) 2{n+1}=2.(3n+3 mod 2) it can be either 0 or 2.

C)
Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1174
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34

### Show Tags

27 Oct 2009, 17:45
1
maliyeci wrote:
{n}=3n mod 2.

options
1) {2n+1)=6n+3 mod 2 that is always equal 1.
2) {2n}+1= 6n mod 2 + 1 that is always equal 1.
3) 2{n+1}=2.(3n+3 mod 2) it can be either 0 or 2.

C)

I couldn't get a single point of it. I think this is something modular arithmetic, which I have no idea. Is there any other way of solving the question, but the problem is that I didn't pick the question either.
_________________
VP
Joined: 05 Mar 2008
Posts: 1353

### Show Tags

28 Oct 2009, 09:24
andrewng wrote:
If {n} denote the remainder when 3n is divided by 2 then which of the following is equal to 1 for all positive integers n?

I/ {2n+1}
II/ {2n}+1
III/ 2{n+1}

A/ I only
B/ II only
C/ I and II
D/ III only
E/ II and III

I don't really understand what it asking for in the question. Could somebody help?

Substitute 2 for each answer and solve..as a check do the same with value of 1
{2} remainder = 0
{1} remainder = 1

I. {2(2) + 1} = {5} plug in 5 into 3n/2 and remainder = 1
II. {2(2} + 1 = {4} remainder = 0 and add 1 so answer = 1
III. 2{2+1} = {3} remainder = 1 but then multiply that by 2 and answer is 2

I. {2(1) +1} = {3} remainder = 1
II. {2(1} + 1 = {2} remainder = 0 and add 1 so answer is 1
III. 2{1+1} = {2} remainder = 0 then multiply by two answer is 0

someone double-check my logic...not 100% sure if correct
Senior Manager
Joined: 23 Jun 2009
Posts: 296
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

### Show Tags

29 Oct 2009, 12:33
Hussain15 wrote:
maliyeci wrote:
{n}=3n mod 2.

options
1) {2n+1)=6n+3 mod 2 that is always equal 1.
2) {2n}+1= 6n mod 2 + 1 that is always equal 1.
3) 2{n+1}=2.(3n+3 mod 2) it can be either 0 or 2.

C)

I couldn't get a single point of it. I think this is something modular arithmetic, which I have no idea. Is there any other way of solving the question, but the problem is that I didn't pick the question either.

Yes. It is about modular arithmetic. I think one must learn this before taking gmat.
Senior Manager
Joined: 22 Dec 2009
Posts: 253

### Show Tags

31 Jan 2010, 06:05
maliyeci wrote:
Yes. It is about modular arithmetic. I think one must learn this before taking gmat.

Do you recommend any books which could teach this concept..... I am still not able to understand ur solution
_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~
Senior Manager
Joined: 22 Dec 2009
Posts: 253

### Show Tags

31 Jan 2010, 06:23
maliyeci wrote:
{n}=3n mod 2.

options
1) {2n+1)=6n+3 mod 2 that is always equal 1.
2) {2n}+1= 6n mod 2 + 1 that is always equal 1.
3) 2{n+1}=2.(3n+3 mod 2) it can be either 0 or 2.

C)

How do you get {2n+1} = 6n+3 mod 2 ...... Am confused!
_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~
Math Expert
Joined: 02 Sep 2009
Posts: 58340

### Show Tags

31 Jan 2010, 07:48
1
jeeteshsingh wrote:
maliyeci wrote:
{n}=3n mod 2.

options
1) {2n+1)=6n+3 mod 2 that is always equal 1.
2) {2n}+1= 6n mod 2 + 1 that is always equal 1.
3) 2{n+1}=2.(3n+3 mod 2) it can be either 0 or 2.

C)

How do you get {2n+1} = 6n+3 mod 2 ...... Am confused!

Given {n} = remainder, when 3n is divide by 2.

Which of the following equals to 1:

I. {2n+1} = remainder, when 3(2n+1)=6n+3 is divide by 2. 6n+3 divided by 2 will always give remainder of 1;
II. {2n}+1 = remainder, when 3(2n)=6n is divide by 2 plus 1. Remainder when 6n divided by 2 is 0 plus 1=1;
III. 2{n+1} = 2*(remainder, when 3(n+1)=3n+3 is divide by 2). 3n+3 divided by 2 will give different remainders.

So only I and II equals to 1.
_________________
Manager
Joined: 10 Feb 2010
Posts: 134

### Show Tags

12 Feb 2010, 18:49
C - I and II

3n/2 = 0 or 1
I just substituted 1 in the equations and solved.
Director
Joined: 23 Jan 2013
Posts: 525
Schools: Cambridge'16
Re: If {n} denote the remainder when 3n is divided by 2 then  [#permalink]

### Show Tags

23 Sep 2015, 22:48
3n/2 gives remander 0 or 1, should recognize the pattern

{1}=1
{2}=0
{3}=1
{4}=0
any odd n gives 1, and any even n gives 0

I. {2n+1} it is always odd, so =1
II.{2n}+1, the same as I, so=1
III. 2{n+1}, it is even, so=0

C
Senior Manager
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: If {n} denote the remainder when 3n is divided by 2 then  [#permalink]

### Show Tags

28 Nov 2016, 01:34
andrewng wrote:
If {n} denote the remainder when 3n is divided by 2 then which of the following is equal to 1 for all positive integers n?

I. {2n+1}
II. {2n}+1
III. 2{n+1}

A. I only
B. II only
C. I and II
D. III only
E. II and III

3 has a remainder 1 when divided by 2

$$\frac{3*n}{2} = \frac{1*n}{2} = \frac{n}{2}$$

We need to take into considerration only $$n$$.

I. {2n+1} = $$\frac{2n+1}{2} = 0*n + 1 = 1$$ Positive

II. {2n}+1 = $$\frac{2n}{2} + 1 = 0 + 1 = 1$$ Positive

III. 2{n+1} = $$2* \frac{n+1}{2}$$ => $$(n+1)$$ can be either odd or evn Negative.

Opions I and II
Non-Human User
Joined: 09 Sep 2013
Posts: 13162
Re: If {n} denote the remainder when 3n is divided by 2 then  [#permalink]

### Show Tags

12 Feb 2019, 00:58
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 {n} denote the remainder when 3n is divided by 2 then   [#permalink] 12 Feb 2019, 00:58
Display posts from previous: Sort by