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

Question

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

mrsmarthi · Accepted Answer

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.

maliyeci · Answer

{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)

Hussain15 · Answer

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.

lagomez · Answer

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

maliyeci · Answer

Yes. It is about modular arithmetic. I think one must learn this before taking gmat.

jeeteshsingh · Answer

Do you recommend any books which could teach this concept..... I am still not able to understand ur solution :oops:

jeeteshsingh · Answer

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

Bunuel · Answer

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.

testprep2010 · Answer

C - I and II

3n/2 = 0 or 1
I just substituted 1 in the equations and solved.

Temurkhon · Answer

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

vitaliyGMAT · Answer

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

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

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