It is currently 18 Oct 2017, 11:39

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 21 Jul 2012
Posts: 11

Kudos [?]: 11 [0], given: 17

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

### Show Tags

02 Jan 2013, 09:00
3
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:48) correct 35% (01:29) wrong based on 238 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Kudos [?]: 11 [0], given: 17

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1377

Kudos [?]: 1675 [1], given: 62

Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

### Show Tags

02 Jan 2013, 09:34
1
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

Do mention the source
_________________

Kudos [?]: 1675 [1], given: 62

Manager
Joined: 18 Oct 2011
Posts: 90

Kudos [?]: 91 [0], given: 0

Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
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.

Kudos [?]: 91 [0], given: 0

Current Student
Joined: 06 Sep 2013
Posts: 1978

Kudos [?]: 719 [0], given: 355

Concentration: Finance
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

Hope this helps
Cheers
J

Kudos [?]: 719 [0], given: 355

Manager
Joined: 18 May 2014
Posts: 63

Kudos [?]: 20 [1], given: 6

Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE: Analyst (Consulting)
Re: If x is a positive integer, is the remainder 0 when (3x + 1) [#permalink]

### Show Tags

18 May 2014, 10:27
1
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.

Kudos [?]: 20 [1], given: 6

Current Student
Joined: 26 Mar 2014
Posts: 99

Kudos [?]: 25 [0], given: 10

Concentration: General Management, Strategy
GMAT 1: 630 Q49 V26
GMAT 2: 710 Q50 V37
WE: Consulting (Computer Software)
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.

Kudos [?]: 25 [0], given: 10

Intern
Joined: 12 Dec 2013
Posts: 17

Kudos [?]: 9 [1], given: 34

If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

07 Nov 2014, 12:20
1
KUDOS
5
This post was
BOOKMARKED
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

Kudos [?]: 9 [1], given: 34

Manager
Joined: 23 Oct 2014
Posts: 103

Kudos [?]: 57 [1], given: 66

Concentration: Marketing
Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

07 Nov 2014, 15:02
1
KUDOS
Quote:
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

With the equation involving 3^x+1, 3^+1 needs to end with a 0 for the equation to be divisible by 10. This can only happen if 3^x ends with a 9.

If you look at all the power of 3's, the unit digit repeats every power of 4.
3^1=ones digit is 3
3^2=ones digit is 9
3^3=ones digit is 7
3^4=ones digit is 1

1. With x=3n+2, I plugged in random numbers
n=1; x=3(1)+2=5; plugging 5 into the equation given...
(3^5+1)/10 is not divisible by 10, because 3^5 will end with a 3 as the ones digit.

n=8; x=3(8)+2=26; plugging 26 into the equation given...
(3^26+1)/10 is divisible by 10, because 3^26 will end with a 9 as the ones digit.

Not Sufficient

2. x>4
Not sufficient.
You can easily test this out by using x=26 or 5 from above.

From using x=26 or 5 you already know that both statements together are not sufficient.

The answer is E.

Kudos [?]: 57 [1], given: 66

Intern
Joined: 22 Feb 2014
Posts: 30

Kudos [?]: 10 [1], given: 3

Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

07 Nov 2014, 17:35
1
KUDOS
1
This post was
BOOKMARKED
The remainder in this division will be zero only when the 3^x term ends in 9. Remember, 3^2, 3^6, 3^10 etc end in 9. So the trend is, 4k+2 where k = 0,1,2,3....

1) x = 3n+2 - 2,5,8,11 etc - clearly, the remainder will be 0 when x = 2 and not 0 when x = 5,8,11 - So not sufficient
2) x > 4 - again, when x = 6 remainder = 0, when x = 5, remainder <> 0 - So not sufficient

Combining 1 & 2: 3n+2 > 4 or n = 1,2,3, etc so, X can take values 5,8,11,14,17,20 - 3^5 + 1 will leave 2 as remainder. 3^14+1 - will leave 0 as remainder (14 = 4*3+1 - fits the trend above). So, given information isn't suitable to answer this question.

Hope this helps.

K

Kudos [?]: 10 [1], given: 3

Director
Joined: 25 Apr 2012
Posts: 724

Kudos [?]: 847 [1], given: 724

Location: India
GPA: 3.21
WE: Business Development (Other)
Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

07 Nov 2014, 22:15
1
KUDOS
Rca 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

Dear Bunuel, need your help! Thank you!

Given x is a positive integer
Note that when x=2, then the expression (3^x+1)/10 will give remainder 0
when x=6 then 3^x=729 so 3^x+1=730 /10 will give remainder 0

St 1 says x=3n+2...possible values of x=2,5,8,11 and 14...
So x=2 R(0),x=3,R not equal to 0..

Not sufficient

St 2 says x>4...x=5 Remainder not zero but if x=6,Remainder zero..

two options..

On combining we have that x>4 and we can have R(0) and $$R \neq{0}$$

Ans E
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 847 [1], given: 724

Math Expert
Joined: 02 Sep 2009
Posts: 41888

Kudos [?]: 128750 [0], given: 12182

Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

09 Nov 2014, 05:35
Expert's post
1
This post was
BOOKMARKED
Rca 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

Dear Bunuel, need your help! Thank you!

Similar question to practice: if-x-is-a-positive-integer-is-the-remainder-0-when-3-x-109075.html
_________________

Kudos [?]: 128750 [0], given: 12182

Manager
Joined: 13 Dec 2013
Posts: 59

Kudos [?]: 30 [0], given: 34

Location: Iran (Islamic Republic of)
Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

09 Jan 2015, 01:23
The Official answer is NOT CORRECT. The answer is Certainly is A...

DATA #1 ) says that IF N Is a POSITIVE INTEGER (SO n CANNOT BE 0) So if we place 1,2 ,3 ,..... in the place of n in the equation we get following pattern respectly as: 5,8.11,.....

so 3^5 + 1 Is not giving ZERO Remaining after diving by 10. also this pattern is continues if we place 8, 11, 14,..... so The answer is NO... the remaining is not 0 when we divide (3^n+1) By 10 so this data is defenetly sufficient...

DATA#2 ) is obviously not sufficient

so Answer IS A NOT E...

Here the official answer should be modified

Kudos [?]: 30 [0], given: 34

Math Expert
Joined: 02 Sep 2009
Posts: 41888

Kudos [?]: 128750 [0], given: 12182

Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

09 Jan 2015, 03:12
The Official answer is NOT CORRECT. The answer is Certainly is A...

DATA #1 ) says that IF N Is a POSITIVE INTEGER (SO n CANNOT BE 0) So if we place 1,2 ,3 ,..... in the place of n in the equation we get following pattern respectly as: 5,8.11,.....

so 3^5 + 1 Is not giving ZERO Remaining after diving by 10. also this pattern is continues if we place 8, 11, 14,..... so The answer is NO... the remaining is not 0 when we divide (3^n+1) By 10 so this data is defenetly sufficient...

DATA#2 ) is obviously not sufficient

so Answer IS A NOT E...

Here the official answer should be modified

That's not correct.

If n = 1, then the remainder when 3^(3*1+2) + 1 is divided by 10 is 4.

If n = 4, then the remainder when 3^(3*4+2) + 1 is divided by 10 is 0.
_________________

Kudos [?]: 128750 [0], given: 12182

Intern
Joined: 29 Sep 2014
Posts: 5

Kudos [?]: 2 [0], given: 2

Concentration: Healthcare, Human Resources
GMAT 1: 650 Q43 V39
If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

09 Jan 2015, 03:21
A is the answer.
S1.
As x=3n+2 , x will be always even and Odd^ Even will always be even as n is not equal to 0. Hence, S1 is sufficient to answer the question.
S2.
x>4 give no information hence B gone.

Hence, the eventual answer is A.
Please correct me if I'm wrong some where.

Kudos [?]: 2 [0], given: 2

Manager
Joined: 13 Dec 2013
Posts: 59

Kudos [?]: 30 [0], given: 34

Location: Iran (Islamic Republic of)
If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

09 Jan 2015, 10:21
Dear Bunuel Please Correct me if I'm wrong..

in the equation (3^x +1) / 10 the reminder is 0 ONLY X raises to the power of 2,6, 10,14,... for example (3^2 +1 ) is 10 and 10/10 gives the 0 reminder .

AS you know the cyclist pattern in 3 power repeats every 4 times so if 3 raises to the power of 2,6, 10,... gives the unit digit 9 and 9 plus 1 gives unit digit of 0 which is ALWAYS divisible by 10

so here we ONLY we need to know whether x could equal to 2, 6, 10,... OR NOT

STATEMENT number 1 directly give us the answer to this question as it says X= 3n+2 and says that n is POSITIVE integer so X could equal 5,8,11,... we can see that x CANNOT be 2,6,10,...

So this statement is SUfficient ...

AM I right?

Thanks,

Kudos [?]: 30 [0], given: 34

Math Expert
Joined: 02 Sep 2009
Posts: 41888

Kudos [?]: 128750 [0], given: 12182

Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

09 Jan 2015, 10:29
Dear Bunuel Please Correct me if I'm wrong..

in the equation (3^x +1) / 10 the reminder is 0 ONLY X raises to the power of 2,6, 10,14,... for example (3^2 +1 ) is 10 and 10/10 gives the 0 reminder .

AS you know the cyclist pattern in 3 power repeats every 4 times so if 3 raises to the power of 2,6, 10,... gives the unit digit 9 and 9 plus 1 gives unit digit of 0 which is ALWAYS divisible by 10

so here we ONLY we need to know whether x could equal to 2, 6, 10,... OR NOT

STATEMENT number 1 directly give us the answer to this question as it says X= 3n+2 and says that n is POSITIVE integer so X could equal 5,8,11,... we can see that x CANNOT be 2,6,10,...

So this statement is SUfficient ...

AM I right?

Thanks,

No, you are not.

5, 8, 11, 14, 17, 20, ...
2, 6, 10, 14, 18, 22, ...
_________________

Kudos [?]: 128750 [0], given: 12182

Manager
Joined: 13 Dec 2013
Posts: 59

Kudos [?]: 30 [0], given: 34

Location: Iran (Islamic Republic of)
Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

09 Jan 2015, 10:33
Bunuel wrote:
Dear Bunuel Please Correct me if I'm wrong..

in the equation (3^x +1) / 10 the reminder is 0 ONLY X raises to the power of 2,6, 10,14,... for example (3^2 +1 ) is 10 and 10/10 gives the 0 reminder .

AS you know the cyclist pattern in 3 power repeats every 4 times so if 3 raises to the power of 2,6, 10,... gives the unit digit 9 and 9 plus 1 gives unit digit of 0 which is ALWAYS divisible by 10

so here we ONLY we need to know whether x could equal to 2, 6, 10,... OR NOT

STATEMENT number 1 directly give us the answer to this question as it says X= 3n+2 and says that n is POSITIVE integer so X could equal 5,8,11,... we can see that x CANNOT be 2,6,10,...

So this statement is SUfficient ...

AM I right?

Thanks,

No, you are not.

5, 8, 11, 14, 17, 20, ...
2, 6, 10, 14, 18, 22, ...

I see , Thank you very much.....

Kudos [?]: 30 [0], given: 34

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 830 [0], given: 5

Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? [#permalink]

### Show Tags

02 Mar 2017, 18:00
Rca 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

We are given that x is a positive integer and need to determine the remainder when 3^x + 1 is divided by 10. Since we know that 1/10 produces a remainder of 1, we really need to determine the remainder when 3^x is divided by 10. We should keep in mind that the remainder of any integer divided by 10 is equivalent to the units digit of that number, so we need to determine the units digit of 3^x.

Statement One Alone:

x = 3n + 2, where n is a positive integer.

We see that we cannot determine the units digit of 3^n. If n = 1, then 3^x = 3^5, which has a units digit of 3, and thus a reminder of 3 when divided by 10. However, if n = 2, then 3^x = 3^8 has a units digit of 1, and thus a reminder of 1 when divided by 10. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x > 4

Knowing that x is greater than 4 is not sufficient to answer the question.

Statements One and Two Together:

Using the statements together, we still cannot answer the question. We can still use n = 1 and n = 2 to obtain 3^x = 3^5 and 3^x = 3^8, respectively. Since 3^5 and 3^8 have different units digits, the remainder when 3^5 + 1 is divided by 10 and the remainder when 3^8 + 1 is divided by 10 will be different.

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 830 [0], given: 5

Re: If x is a positive integer, is the remainder 0 when (3^x + 1)/10?   [#permalink] 02 Mar 2017, 18:00
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.