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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

11 Feb 2011, 03:34

6

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

alltimeacheiver wrote:

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

Question should be as follows:

If x is a positive integer, is the remainder 0 when 3^(x) + 1 is divided by 10?

(1) x = 4n + 2, where n is a positive integer.

Last digit of \(3^x\) repeats in blocks of 4: {3, 9, 7, 1} - {3, 9, 7, 1} - ... So cyclicity of the last digit of 3 in power is 4. Now, \(3^{4n+2}\) will have the same last digit as \(3^2\) (remainder upon division 4n+2 upon cyclicity 4 is 2, which means that 3^{4n+2} will have the same last digit as 3^2). Last digit of \(3^2\) is \(9\). So \(3^{4n+2}+1\) will have the last digit \(9+1=0\). Number ending with 0 is divisible by 10 (remainder 0). Sufficient.

Re: If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

12 Feb 2011, 13:51

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

looking at the question, we are dealing with even numbers. we know that x has to pos. int. we know that 3x + 1 = odd and we know that 10 is an even number. therefore remainder cannot be zero when divided by 10.

s1, x = 4n + 2. given this eqn in s1, we know that x has to equal an even number. When you substitute the even value of x in 3x + 1, we have an odd number such that it cannot be divisible by 10.

There s1 sufficient.

s2, x > 4. x can have a range of numbers therefore insufficient.

Re: If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

12 Feb 2011, 13:57

Expert's post

maryann wrote:

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

looking at the question, we are dealing with even numbers. we know that x has to pos. int. we know that 3x + 1 = odd and we know that 10 is an even number. therefore remainder cannot be zero when divided by 10.

s1, x = 4n + 2. given this eqn in s1, we know that x has to equal an even number. When you substitute the even value of x in 3x + 1, we have an odd number such that it cannot be divisible by 10.

There s1 sufficient.

s2, x > 4. x can have a range of numbers therefore insufficient.

Ans A.

Original question is: If x is a positive integer, is the remainder 0 when [b]3^(x) + 1 is divided by 10?[/b]

Re: If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

02 Jan 2013, 02:05

Bunuel wrote:

alltimeacheiver wrote:

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

Question should be as follows:

If x is a positive integer, is the remainder 0 when 3^(x) + 1 is divided by 10?

(1) x = 4n + 2, where n is a positive integer.

Last digit of \(3^x\) repeats in blocks of 4: {3, 9, 7, 1} - {3, 9, 7, 1} - ... So cyclicity of the last digit of 3 in power is 4. Now, \(3^{4n+2}\) will have the same last digit as \(3^2\) (remainder upon division 4n+2 upon cyclicity 4 is 2, which means that 3^{4n+2} will have the same last digit as 3^2). Last digit of \(3^2\) is \(9\). So \(3^{4n+2}+1\) will have the last digit \(9+1=0\). Number ending with 0 is divisible by 10 (remainder 0). Sufficient.

(2) x > 4. Clearly insufficient.

Answer: A.

Dear Bunuel,

I have another similar question. All info gave me are almost same. The only difference is in Statement (1): \(x= 3^n+1\). Answer goes to E. I knew that approach should be the same reference "\(4^n+2\)". I look at someone started from 1, 3,9,27,81, xxx3,xxx9,xxxx7,xxxx1, xxxx3, xxxx9, xxxx7, xxxx1, and so on.... And then reasoned that reference, which is \(4^n+2\).

I'm wondering how to quick approach that reference. Can you answer in this thread or should I submit a new post?

Re: If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

02 Jan 2013, 04:12

Expert's post

curtis0063 wrote:

Bunuel wrote:

alltimeacheiver wrote:

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

Question should be as follows:

If x is a positive integer, is the remainder 0 when 3^(x) + 1 is divided by 10?

(1) x = 4n + 2, where n is a positive integer.

Last digit of \(3^x\) repeats in blocks of 4: {3, 9, 7, 1} - {3, 9, 7, 1} - ... So cyclicity of the last digit of 3 in power is 4. Now, \(3^{4n+2}\) will have the same last digit as \(3^2\) (remainder upon division 4n+2 upon cyclicity 4 is 2, which means that 3^{4n+2} will have the same last digit as 3^2). Last digit of \(3^2\) is \(9\). So \(3^{4n+2}+1\) will have the last digit \(9+1=0\). Number ending with 0 is divisible by 10 (remainder 0). Sufficient.

(2) x > 4. Clearly insufficient.

Answer: A.

Dear Bunuel,

I have another similar question. All info gave me are almost same. The only difference is in Statement (1): \(x= 3^n+1\). Answer goes to E. I knew that approach should be the same reference "\(4^n+2\)". I look at someone started from 1, 3,9,27,81, xxx3,xxx9,xxxx7,xxxx1, xxxx3, xxxx9, xxxx7, xxxx1, and so on.... And then reasoned that reference, which is \(4^n+2\).

I'm wondering how to quick approach that reference. Can you answer in this thread or should I submit a new post?

Please post full question in a separate topic. _________________

Re: If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

12 May 2015, 20:14

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 x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

12 May 2015, 22:02

1

This post received KUDOS

Expert's post

alltimeacheiver wrote:

If x is a positive integer, is the remainder 0 when 3^(x) + 1 is divided by 10?

(1) x = 4n + 2, where n is a positive integer. (2) x > 4

Though this is quite an easy question, the accuracy statistics suggest that roughly 1 out of every 4 students who attempted this question got it wrong.

This may have happened because the students first straight-away started from the given statements and then, got confused in processing the question statement and the Statement 1 (and 2) together.

Here's an alternate solution that eliminates the chances of such confusion!

Let's first analyze the question statement alone:

The given expression is \(3^{x} + 1\)

The units digit of 3 can be 3 (for powers of the form 4m+1), 9 (for powers of the form 4m+2), 7 (for powers of the form 4m+3) or 1(for powers of the form 4m)

Out of these 4 possible unit digits, the sum \(3^{x} + 1\) will be divisible by 10 only when the units digit is 9.

So, the question is actually asking us to find if the power of 3, that is x, is of the form 4m + 2 or not.

Now that we've simplified the question, analyzing the 2 statements is going to be a cakewalk!

Please note how the analysis in my solution is quite similar to the analysis in the solutions posted above. The point of difference comes in when I did that analysis. I did it before I went to Statements 1 and 2. The benefit of doing this analysis with the question statement itself is that I now have a very clear idea of what I need to look for, in order to answer the question. And because of this clear idea, the chances of my getting confused by irrelevant information in Statements 1 and 2 are also greatly reduced.

Re: If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

26 May 2016, 04:39

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. _________________

If x is a positive integer, is the remainder 0 when 3^(x) + [#permalink]

Show Tags

26 May 2016, 05:32

This question checks divisibility of 3. Concentrate only on last digit of product and not the entire value.

Now \(3^4\)= 81, i.e. last digit is 1. \(3^5\) has last digit 3.

So \(3^{4x}\) will have "1" as its last digit. [\(3^{4x}\) can be written as (\(3^4\))^x

Statement 1 \(3^{4n+2}\) is nothing but (\(3^{4n}\))* (\(3^2\)). The last digit of this product will be 9. Adding 1 to this sum will yield a zero and so the entire product will be divisible by 10. (1) is sufficient

Statement 2

x>4. x=5 --> This will have last digit of 3's power as 3 [(\(3^4\))*(3) => Last digit will be 3]. Add 3+1 = 4. Not divisible by 10.

x=6 --> This will have last digit of 3's power as 9 [(\(3^4\))*(9) => Last digit will be 9]. Add 9+1 = 10. Will be divisible by 10.

So Statement (B) is not sufficient.

Answer is A

gmatclubot

If x is a positive integer, is the remainder 0 when 3^(x) +
[#permalink]
26 May 2016, 05:32

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

I’m a little delirious because I’m a little sleep deprived. But whatever. I have to write this post because... I’M IN! Funnily enough, I actually missed the acceptance phone...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...