Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 10 Feb 2016, 16:59

### 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:
Director
Joined: 10 Feb 2006
Posts: 657
Followers: 3

Kudos [?]: 252 [0], given: 0

When the positive integer x is divided by 9, the remainder [#permalink]  22 Nov 2007, 17:04
1
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:50) correct 11% (00:43) wrong based on 132 sessions
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, 00:00, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
VP
Joined: 09 Jul 2007
Posts: 1103
Location: London
Followers: 6

Kudos [?]: 86 [0], given: 0

Re: MGMT - Remainder [#permalink]  22 Nov 2007, 17:11
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
Director
Joined: 08 Jun 2007
Posts: 583
Followers: 2

Kudos [?]: 84 [0], given: 0

Re: MGMT - Remainder [#permalink]  22 Nov 2007, 17:32
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
Senior Manager
Joined: 06 Aug 2007
Posts: 368
Followers: 1

Kudos [?]: 27 [0], given: 0

Re: MGMT - Remainder [#permalink]  22 Nov 2007, 19:50
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....
SVP
Joined: 05 Jul 2006
Posts: 1513
Followers: 5

Kudos [?]: 179 [0], given: 39

Re: MGMT - Remainder [#permalink]  02 Dec 2007, 02:40
[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
Manager
Joined: 26 May 2013
Posts: 56
Followers: 0

Kudos [?]: 19 [0], given: 220

Re: MGMT - Remainder [#permalink]  19 May 2014, 19:56
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
Math Expert
Joined: 02 Sep 2009
Posts: 31299
Followers: 5356

Kudos [?]: 62347 [1] , given: 9454

Re: MGMT - Remainder [#permalink]  20 May 2014, 00:16
1
KUDOS
Expert's post
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.
_________________
Intern
Joined: 14 May 2014
Posts: 45
Followers: 0

Kudos [?]: 29 [0], given: 1

Re: When the positive integer x is divided by 9, the remainder [#permalink]  20 May 2014, 02:50
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.

Intern
Joined: 23 Jul 2012
Posts: 6
Followers: 0

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

Re: When the positive integer x is divided by 9, the remainder [#permalink]  26 May 2014, 07:41
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).
Re: When the positive integer x is divided by 9, the remainder   [#permalink] 26 May 2014, 07:41
Similar topics Replies Last post
Similar
Topics:
7 x and y are positive integers. When x is divided by 11, the remainder 6 09 Oct 2015, 01:47
1 When 100 is divided by positive integer x, the remainder is 5 22 Sep 2013, 10:01
19 When positive integer x is divided by 5, the remainder is 3 9 02 Mar 2012, 09:39
27 When positive integer x is divided by 5, the remainder is 3; 20 12 Mar 2008, 12:16
4 When positive integer x is divided by positive integer y, the remainde 4 30 Jun 2007, 08:26
Display posts from previous: Sort by