It is currently 23 Oct 2017, 23:06

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the smallest number which when increased by 3 is divisible by

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41909

Kudos [?]: 129564 [0], given: 12202

What is the smallest number which when increased by 3 is divisible by [#permalink]

Show Tags

New post 01 Dec 2015, 04:36
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:46) correct 22% (01:45) wrong based on 133 sessions

HideShow timer Statistics

Kudos [?]: 129564 [0], given: 12202

Math Forum Moderator
User avatar
D
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1533

Kudos [?]: 959 [0], given: 72

Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: What is the smallest number which when increased by 3 is divisible by [#permalink]

Show Tags

New post 01 Dec 2015, 05:47
1
This post was
BOOKMARKED
Prime factorization of numbers
27 = 3^3
35 = 5*7
25 = 5^2
21 = 3*7

Smallest number divisble by above 4 numbers will be LCM = 3^3 * 5^2 * 7 = 4725
Now , the number we need is 3 less than 4725 , therefore the number is 4722

Answer D
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Kudos [?]: 959 [0], given: 72

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

Kudos [?]: 1088 [0], given: 325

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: What is the smallest number which when increased by 3 is divisible by [#permalink]

Show Tags

New post 01 Dec 2015, 12:21
The problem can be reduced if we add 3 to the answer options and check divisibility rule of 3 ( Since 27 is a multiple of 3)

I am deliberately not involving in checking the divisibility rule for 5 and 7 since all the answer options have units digit as 5 and divisibility by 7 is a cumbersome 3 step process, where as divisibility by 3 is simply the sum of all the digits of the number.


(A) 3272 -> 3272+3 = 3275 Sum of the digits is 17 which is not divisible by 3.

(B) 3572 -> 3572+3 = 3575 Sum of the digits is 20 which is not divisible by 3.


(C) 4122 -> 4122+3 = 4125 Sum of the digits is 12 which is divisible by 3 { Keep this option for now }

(D) 4722 -> 4722+3 = 4725 Sum of the digits is 18 which is divisible by 3 { Keep this option for now }


(E) 4922 -> 4922+3 = 4925 Sum of the digits is 20 which is not divisible by 3

Now check options (C) and (D)

C) 4125 / 27 = Not completely divisible , so this is not the answer.

D) 4725 / 27 = 175 Completely divisible , so this is our answer.
_________________

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 [?]: 1088 [0], given: 325

Director
Director
avatar
D
Joined: 22 Jun 2014
Posts: 896

Kudos [?]: 423 [0], given: 111

Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Premium Member CAT Tests
Re: What is the smallest number which when increased by 3 is divisible by [#permalink]

Show Tags

New post 01 Dec 2015, 13:37
We need the highest power of each prime from all the numbers given.

3 comes 3 times in 27

5 and 7 comes once in 35

5 comes twice in 25

3 and 7 comes once in 21.

so we need three 3's, two 5's and one 7 for a number to be divisible by 27, 35, 25 and 21.

number = 3*3*3*5*5*7 = 4725

correct answer choice would be 3 less than this number because in question it give that "smallest number which when increased by 3"

Hence 4722 i.e. "D" is the correct answer.
_________________

---------------------------------------------------------------
Target - 720-740
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

Kudos [?]: 423 [0], given: 111

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16525

Kudos [?]: 274 [0], given: 0

Premium Member
Re: What is the smallest number which when increased by 3 is divisible by [#permalink]

Show Tags

New post 22 May 2017, 18:55
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

Kudos [?]: 274 [0], given: 0

Manager
Manager
User avatar
S
Joined: 22 May 2015
Posts: 78

Kudos [?]: 16 [0], given: 22

Re: What is the smallest number which when increased by 3 is divisible by [#permalink]

Show Tags

New post 06 Sep 2017, 18:06
I used the divisibility test for 9 ( any number which is divisible by 9 has it's sum of digits equal to 9 ) and found out only Option D satisfies this condition.
_________________

Consistency is the Key

Kudos [?]: 16 [0], given: 22

Re: What is the smallest number which when increased by 3 is divisible by   [#permalink] 06 Sep 2017, 18:06
Display posts from previous: Sort by

What is the smallest number which when increased by 3 is divisible by

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.