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 (3x + 1) [#permalink]

Show Tags

02 Jan 2013, 09:34

1

This post received KUDOS

curtis0063 wrote:

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

The remainder will be zero when x is \(4n-2\) i.e. 2, 6, 10, 14 etc. Statement 1 tells us that x=5, 8,11, 14 etc Not sufficient statement 2 is not sufficient On combinng also, the information is not sufficient. Hence +1E

Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

Show Tags

03 Jan 2013, 14:26

The powers of 3 are as follows: 3,9,27,81,243,729.....The pattern of the units digit is 3,9,7,1,3......

The only way the expression would result in a remainder of 0 is if the numerator is a factor of 10. For that to happen x would need to be 2,6,10,14...and so on.

From statement 1: If n is 4 then there would be a remainder of 0. But if n was 3 that would not hold true From statement 2: Clearly not sufficient. 1+2 Together still not sufficient.

Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

Show Tags

23 Feb 2014, 09:18

OK first thing's first. We need to know if the expression 3^x + 1 will be divisible by 10 which means that we need to know if units digit will be zero. Now, 3^x has cycle 3,9,7,1 so only if the units digit is in the second place (9) we will get UD of zero. Let's find out if this can be the case.

First statement, x = 3n + 2. Now we are told that n must be a positive integer. We have the following options 5,8,11,14,17,20 etc....for the exponent. If we divide by 4 and gauge the remainders we will get that remainder can be 3,1,7,9 and then the cycle repeats again. Therefore insufficient.

Second Statement tells us that x>4, well this is insufficient because the cycle repeats itself. Both together, statement 2 wasn't helpful at all so this is going to be a clear E

Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

Show Tags

18 May 2014, 10:27

1

This post received KUDOS

Stmt II

x > 4

x=5 3x+1 is 16 then remainder is 6 x=6 3x+1 is 17 then remainder is 7

x can take on many more values for which the remainder value varies(could be x=243 then remainder is 0)

INSUFFICIENT

Stmt I

x = 4n+2

3X+1 = 3(4N+2) = 12N+7

12n+7 will never be divisible by 10 since the units digit of 12*some positive integer n will never be 3 (only if the units digit is 3 will the resulting number when added to 7 have a units digit of 0 to be divisible by 10)

Units digit for 12* n will cycle as follows 2,4,6,8,0,2,4...etc

Since its a yes or no question we can confidently say NO which makes this statement SUFFICIENT to answer the question Hence E.

Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

Show Tags

26 May 2014, 13:55

Marcab wrote:

curtis0063 wrote:

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

The remainder will be zero when x is \(4n-2\) i.e. 2, 6, 10, 14 etc. Statement 1 tells us that x=5, 8,11, 14 etc Not sufficient statement 2 is not sufficient On combinng also, the information is not sufficient. Hence +1E

Do mention the source

How do you get that remainder will be zero when x=4n - 2 ? Could you elaborate a little further on this point? Thanks! Cheers J

Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

Show Tags

27 May 2014, 21:02

Basically , when divisor is 10 the remainder will be 0 when the numerator has a 0 in the units digit.

The numerator here is 3^x + 1 . So this means when the units digit of 3 ^x is 9 then the units digit of the complete numerator will be 0. Now lets see in what circumstances will the units digit of 3^x will be 9.

3^1 - Units digit is 3 3^2 - Units digit is 9 3^3 - Units digit is 7 3^4 - Units digit is 1 3^5 - Units digit is 3

So we see that the cyclisity is 4 and the units digit will be 9 on the second iteration. So cyclisity is 4n and units digit is 9 on 4n - 2. I am guessing this is how Marcab reached the conclusion that remainder will be 0 when X = 4n - 2.

Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

Show Tags

13 Sep 2016, 13:13

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.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

There is without a doubt a stereotype for recent MBA grads – folks who are ambitious, smart, hard-working, but oftentimes lack experience or domain knowledge. Looking around and at...