GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Nov 2018, 10:15

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50619
What is the smallest number which when increased by 3 is divisible by  [#permalink]

Show Tags

New post 01 Dec 2015, 03:36
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:47) correct 20% (01:49) wrong based on 203 sessions

HideShow timer Statistics

Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2114
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
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, 04:47
1
1
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

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4212
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, 11:21
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 )

Moderator
avatar
V
Joined: 21 Jun 2014
Posts: 1053
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
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, 12:37
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
Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html
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

Manager
Manager
User avatar
G
Joined: 22 May 2015
Posts: 104
Re: What is the smallest number which when increased by 3 is divisible by  [#permalink]

Show Tags

New post 06 Sep 2017, 17:06
1
1
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

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: What is the smallest number which when increased by 3 is divisible by  [#permalink]

Show Tags

New post 23 Oct 2018, 18:25
Bunuel wrote:
What is the smallest number which when increased by 3 is divisible by 27, 35, 25 and 21?

(A) 3272

(B) 3572

(C) 4122

(D) 4722

(E) 4922


Let’s first determine the LCM of 27, 35, 25, and 21

27 = 3^3

35 = 5 x 7

25 = 5^2

21 = 3 x 7

So the LCM is 3^3 x 5^2 x 7 = 4,725. Since the number sought needs to be increased by 3 to become 4,725, so that number is 4,725 - 3 = 4,722.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

GMAT Club Bot
Re: What is the smallest number which when increased by 3 is divisible by &nbs [#permalink] 23 Oct 2018, 18:25
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.