It is currently 18 Oct 2017, 05:00

### 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

# When the positive integer x is divided by 9, the remainder

Author Message
TAGS:

### Hide Tags

Director
Joined: 10 Feb 2006
Posts: 660

Kudos [?]: 621 [1], given: 0

When the positive integer x is divided by 9, the remainder [#permalink]

### Show Tags

22 Nov 2007, 18:04
1
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

87% (00:40) correct 13% (00:40) wrong based on 312 sessions

### HideShow timer Statistics

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6
[Reveal] Spoiler: OA

_________________

GMAT the final frontie!!!.

Last edited by Bunuel on 20 May 2014, 01:00, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.

Kudos [?]: 621 [1], given: 0

VP
Joined: 09 Jul 2007
Posts: 1098

Kudos [?]: 141 [1], given: 0

Location: London

### Show Tags

22 Nov 2007, 18:11
1
KUDOS
1
This post was
BOOKMARKED
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6

thanks

X=9K+5

3X=3(9K+5)

then

(27K+15)/9
3K+15/9
15/9 ends with remainder 6.

E
also plug any number into K to test

Kudos [?]: 141 [1], given: 0

Director
Joined: 08 Jun 2007
Posts: 575

Kudos [?]: 109 [0], given: 0

### Show Tags

22 Nov 2007, 18:32
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6

thanks

6
Plugging is simple here.

x = 9k + 5
for k =1 x = 14
3x = 42 . Divide by 9 , you get remainder 6.
Same with k=2 and other k's

Kudos [?]: 109 [0], given: 0

Senior Manager
Joined: 06 Aug 2007
Posts: 360

Kudos [?]: 35 [0], given: 0

### Show Tags

22 Nov 2007, 20:50
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6

thanks

lets say the quotient is y.

So from the first part 9y+ 5 = x

so 3x = 27y + 15(remainder)

since 15 when divided by 9 gives you 6....

Kudos [?]: 35 [0], given: 0

SVP
Joined: 05 Jul 2006
Posts: 1750

Kudos [?]: 430 [0], given: 49

### Show Tags

02 Dec 2007, 03:40
[quote="alimad"]When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6

x= 9k+5 ie: 3x = 27k+15, 27k+15 / 9 = a reminder of 15-9 = 6

Kudos [?]: 430 [0], given: 49

Intern
Joined: 29 Apr 2011
Posts: 25

Kudos [?]: 3 [0], given: 0

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

### Show Tags

29 Apr 2011, 22:47
plug in nos.

Let x = 14, 23, 32
x/9
Reminder is 5

Let 3x = 3*14, 3*23, 3*32
3x/9
Reminder is 6

Kudos [?]: 3 [0], given: 0

SVP
Joined: 16 Nov 2010
Posts: 1598

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology
Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

### Show Tags

29 Apr 2011, 23:32
x= 9k + 5

=> 3x = 27k + 15

=> 3x = 27k + 9 + 6

=> 3x/9 = 9(3k + 1)/9 + 6/9

So remainder is 6

Otherwise, just take 5 as an example :

So 5/9 = remainder 5

15/9 = remainder 6

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 592 [0], given: 36

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1285

Kudos [?]: 281 [0], given: 10

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

### Show Tags

29 Apr 2011, 23:35
x = 9 * q + 5
3x = 27 *q + 15

15-9 = 6. Hence the remainder is 6. Which is less than 9.

If suppose
x = 9 *q + 7
3x = 27 * q + 21

Remainder will be 21-9*2 = 3.

E.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Kudos [?]: 281 [0], given: 10

Director
Joined: 01 Feb 2011
Posts: 726

Kudos [?]: 143 [0], given: 42

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

### Show Tags

30 Apr 2011, 15:07
i tried plugging in numbers

x = 9q+5

x = 14

3x = 42 = 36 + 6 = 9*4+6

remainder is 6.

Kudos [?]: 143 [0], given: 42

Manager
Joined: 26 May 2013
Posts: 65

Kudos [?]: 38 [0], given: 243

### Show Tags

19 May 2014, 20:56
Are we not supposed to reduce the fraction in such questions? I'm getting 2 as a remainder to this problem. I reduced 42/9 to 14/3 leaving 2 as the remainder. Please point out my error.

Thanks

yezz wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6

x= 9k+5 ie: 3x = 27k+15, 27k+15 / 9 = a reminder of 15-9 = 6

Kudos [?]: 38 [0], given: 243

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128688 [1], given: 12182

### Show Tags

20 May 2014, 01:16
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
Amit0507 wrote:
Are we not supposed to reduce the fraction in such questions? I'm getting 2 as a remainder to this problem. I reduced 42/9 to 14/3 leaving 2 as the remainder. Please point out my error.

Thanks

42 divided by 9 gives the reminder of 6. If you reduce 42/9 by 3 to 14/3, then the remainder you get dividing 14 by 3 is 2. The remainders are not the same which means that this approach is not correct. Actually the remainder will be 3 times as great (by the factor you reduced), so 6.

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6

Approach 1:

When the positive integer x is divided by 9, the remainder is 5: $$x=9q+5$$.

$$3x=27q+15$$. Now, 27 is divisible by 9, so the remainder is obtained only by division 15 by 9. 15 gives the remainder of 6 upon dividing by 9.

Approach 2:

When the positive integer x is divided by 9, the remainder is 5 --> let x=5. Then 3x=15. 15 divided by 9 gives the remainder of 6.

Theory on remainders problems: remainders-144665.html

Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

Hope this helps.
_________________

Kudos [?]: 128688 [1], given: 12182

Intern
Joined: 14 May 2014
Posts: 45

Kudos [?]: 51 [0], given: 1

Re: When the positive integer x is divided by 9, the remainder [#permalink]

### Show Tags

20 May 2014, 03:50
Lets take the number as x

when x is divided by 9 the remainder is 5 hence x can be written as

x=9k +5

Multiplying by 3 will give

3x = 27k + 15

we can also write
3x = 27k + 9 + 6

Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
_________________

Help me with Kudos if it helped you "

Mathematics is a thought process.

Kudos [?]: 51 [0], given: 1

Intern
Joined: 23 Jul 2012
Posts: 6

Kudos [?]: 3 [0], given: 2

Re: When the positive integer x is divided by 9, the remainder [#permalink]

### Show Tags

26 May 2014, 08:41
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6

dividend = quotient * divisior + R
so, x = q * 9 + 5
so, q * 9 = x - 5

also, 3x = 9 * q + R
so, q * 9 = 3x - R

Thus, 3x - R = x - 5
so, R = 2x + 5

Now x cannot be 0 or a negative number (as its given that it is positive). Thus, whatever the answer is, its greater than 5.
As per the answer choices, only 6 is greater than 5. Thus we have answer as 6 (choice E).

Kudos [?]: 3 [0], given: 2

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16713

Kudos [?]: 273 [0], given: 0

Re: When the positive integer x is divided by 9, the remainder [#permalink]

### Show Tags

25 Mar 2016, 03:43
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.
_________________

Kudos [?]: 273 [0], given: 0

Senior Manager
Status: DONE!
Joined: 05 Sep 2016
Posts: 408

Kudos [?]: 23 [0], given: 283

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

### Show Tags

16 Oct 2016, 12:37
E is correct. Here's why:

From the prompt we can create the following equation:

x=9y+5

Now, let's say y = 0 --> then x = 5 --> plug this into 3x --> 3x = 15

15/9 = 1 Remainder 6

Kudos [?]: 23 [0], given: 283

Director
Joined: 05 Mar 2015
Posts: 964

Kudos [?]: 287 [0], given: 41

Re: When the positive integer x is divided by 9, the remainder [#permalink]

### Show Tags

16 Oct 2016, 13:03
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6

Attachments

22.png [ 8.67 KiB | Viewed 3417 times ]

Kudos [?]: 287 [0], given: 41

Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1087 [0], given: 325

Location: India
GPA: 3.5
Re: When the positive integer x is divided by 9, the remainder [#permalink]

### Show Tags

16 Oct 2016, 13:44
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6

Least possible number of x is 5

So, 3x = 15

$$\frac{15}{9}$$ = Remainder 6

Hence correct answer will be (E) 6

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1087 [0], given: 325

SVP
Joined: 08 Jul 2010
Posts: 1834

Kudos [?]: 2276 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: When the positive integer x is divided by 9, the remainder [#permalink]

### Show Tags

10 Jul 2017, 23:28
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6

*Test like approach:*
choose a number that satisfies the given constraint I'm. Remainder 5 when divided by 9.
Such number, x = 5, 14, 23 etc.

Choose smallest and find 3x
I.e. 3x= 15
Divide by 9 and check remainder = 6

*Point to learn*
A number when divided by 9 leaves remainder 5 will be of the form = 9a+5

I.e. x= 9a+5

Now 3x = 3(9a+5)= 27a+15

When 3x is divided by 9 then 27a is always divisible hence remainder will be obtained by getting the remainder when 15 is divided by 9

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2276 [0], given: 51

Re: When the positive integer x is divided by 9, the remainder   [#permalink] 10 Jul 2017, 23:28
Display posts from previous: Sort by