NEW HERE? LEARN MORE
close
It is currently 01 Feb 2023, 14:28
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

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
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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

A positive integer is divisible by 3 if and only if the sum

29 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
   1   2 
User avatar
P
energetics
Senior Manager
Senior Manager
Joined: 05 Feb 2018
Posts: 344
A positive integer is divisible by 3 if and only if the sum [#permalink] New post  01 Jun 2019, 10:23
cf92 wrote:
Am I the only one who found the question confusing? It asked "how many values could N have" - not K. I understand K can take 4 values, but doesn't any combination of 0, 3, 6, 9 mean a different value for N?


Maybe it's a typo because the OA on GMATPrep only talks about the value of k but the answer is the same because it says k is the same digit in both spaces (so only 4 choices).
If k could be a different digit then n would have 4*4 = 16 different values divisible by 3.
avatar
P
sayan640
Manager
Manager
Joined: 29 Oct 2015
Posts: 244
Re: A positive integer is divisible by 3 if and only if the sum [#permalink] New post  29 Sep 2019, 15:12
NoHalfMeasures wrote:
A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 1k2,k24, where k represents a digit that occurs twice, how many values could n have?

A 2
B. 3
C. 4
D. 5
E 10


n is of the form :- 1k2k24 ....
Some of the digits except k :- 1 + 2 + 2 + 4 = 9
So for n to be divisible by 3 , k can take :- 0 or 3 or 6 or 9 . (4 values)
So one 'k' can be of 4 kinds and for each kind , another 'k' can be of that kind only ( similar to it ) i.e 1 kind.
So the number 'n' can be of :- 4 *1 = 4

Option C is the answer.
Please give me kudo s if you liked my explanation.
User avatar
G
Ravixxx
Manager
Manager
Joined: 24 Feb 2020
Posts: 129
Location: Italy
WE:Analyst (Investment Banking)
A positive integer is divisible by 3 if and only if the sum [#permalink] New post  24 Apr 2020, 00:43
SOLUTION:
A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

1 K 2 K 2 4
9+ K + K

K= 0: 9+0+0 = 9 divisible by 3.
K= 1: 9+1+1 = 11 it is not divisible by 3.
K= 2: 9+2+2 = 13 it is not divisible by 3
K= 3: 9+3+3 = 15 divisible by 3
K= 4: 9+4+4 = 17 it is not divisible by 3.
K= 5: 9+5+5 = 19 it is not divisible by 3
K= 6: 9+6+6 = 21 divisible by 3
K= 7: 9+7+7 = 23 it is not divisible by 3.
K= 8: 9+8+8 = 25 it is not divisible by 3.
K= 9: 9+9+9 = 27 divisible by 3.

K could be: {0,3,6,9} 4 values.

ANSWER C
User avatar
P
Mizar18
Manager
Manager
Joined: 28 Jan 2019
Posts: 186
Location: Peru
Re: A positive integer is divisible by 3 if and only if the sum [#permalink] New post  31 Aug 2020, 16:57
1k2,k24 is a number divisible by 3, so 1+2+2+4+2K =multiple of 3:

9+2K= multiple of 3. Since we know that 9 is a multiple of 3, 2K must be also a multiple of 3, so, possible values are:
0, 3,6, and 9.

C) is the answer.
_________________
Make your mercy overcome your wrath
Signature Read More
User avatar
P
Mizar18
Manager
Manager
Joined: 28 Jan 2019
Posts: 186
Location: Peru
Re: A positive integer is divisible by 3 if and only if the sum [#permalink] New post  31 Aug 2020, 17:00
cf92 wrote:
Am I the only one who found the question confusing? It asked "how many values could N have" - not K. I understand K can take 4 values, but doesn't any combination of 0, 3, 6, 9 mean a different value for N?


I do not think so, it is clearly stated that the number 1k2, k24, has a digit that occurs twice

best.
_________________
Make your mercy overcome your wrath
Signature Read More
User avatar
P
Basshead
VP
VP
Joined: 09 Jan 2020
Posts: 1058
Location: United States
Re: A positive integer is divisible by 3 if and only if the sum [#permalink] New post  17 Nov 2020, 03:44
NoHalfMeasures wrote:
A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 1k2,k24, where k represents a digit that occurs twice, how many values could n have?

A 2
B. 3
C. 4
D. 5
E 10


We have a 6 digit integer: 1k2,k24

The 4 given digits sum to 9. This means for this number to be divisible by 3, 9 + 2k must be divisible by three.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

0, 3, 6, and 9 all work. Answer is C.
_________________
Help me get better -- please critique my responses!
Signature Read More
avatar
B
RahulSriniChelsea
Intern
Intern
Joined: 23 Apr 2020
Posts: 6
Re: A positive integer is divisible by 3 if and only if the sum [#permalink] New post  17 Nov 2020, 04:25
An easy question only made difficult in the fact that many people would have ignored the '0'. Nevertheless, practice makes perfect!
avatar
B
Sagart21
Manager
Manager
Joined: 25 Oct 2020
Posts: 51
Location: India
Concentration: Strategy, General Management
Re: A positive integer is divisible by 3 if and only if the sum [#permalink] New post  17 Nov 2020, 04:45
NoHalfMeasures wrote:
A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 1k2,k24, where k represents a digit that occurs twice, how many values could n have?

A 2
B. 3
C. 4
D. 5
E 10


1+2+2+4 = 9 which is divisible by 3
So 2k can take values which are multiples of 3
So k = 0,3,6,9
Ans: C.4
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 26466
Re: A positive integer is divisible by 3 if and only if the sum [#permalink] New post  27 Dec 2022, 22:27
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.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: A positive integer is divisible by 3 if and only if the sum [#permalink]
27 Dec 2022, 22:27
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
   1   2 
Moderators:
chetan2u
Math Expert
10657 posts
Bunuel
Math Expert
88502 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3130 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions