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

It is currently 19 Oct 2019, 15:14

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

The greatest number of four digits which is divisible by 15, 25, 40 an

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
G
Joined: 29 Jun 2018
Posts: 53
Location: India
GPA: 4
GMAT ToolKit User
The greatest number of four digits which is divisible by 15, 25, 40 an  [#permalink]

Show Tags

New post Updated on: 10 Aug 2018, 00:19
5
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (01:49) correct 28% (01:26) wrong based on 90 sessions

HideShow timer Statistics

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000
B. 9400
C. 9600
D. 9800
E. 9999

_________________

Originally posted by LMP on 09 Aug 2018, 02:53.
Last edited by Bunuel on 10 Aug 2018, 00:19, edited 1 time in total.
Renamed the topic.
VP
VP
User avatar
D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: The greatest number of four digits which is divisible by 15, 25, 40 an  [#permalink]

Show Tags

New post 09 Aug 2018, 03:20
3
Bulusuchaitanya wrote:
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000
B. 9400
C. 9600
D. 9800
E. 9999


Since the 4-digit number is divisible by 15, 25, 40 and 75. So, the number must be divisible by LCM( 15, 25, 40 ,75)=600.

The greatest 4-digit number in number system is 9999.

So, the required number=9999-Rem(\(\frac{9999}{600}\))=9999-399=9600

Ans. (C)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7984
Re: The greatest number of four digits which is divisible by 15, 25, 40 an  [#permalink]

Show Tags

New post 09 Aug 2018, 04:51
1
Bulusuchaitanya wrote:
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000
B. 9400
C. 9600
D. 9800
E. 9999



the choices straight away give you the answer..
the number has to be multiple of 5 and 2, so has to have 0 as units digit... eliminate E
the number is also a multiple of 3, so the sum of digits of number must be divisible by 3...
9800=9+8+0+0=17.. NOT divisible by 3 so eliminate D
9600 = 9+6+0+0=15...div by 3, so our answer
C

Also the question is basically asking for multiple of the LCM of 15,25,40 and 75
\(15=3*5...........
25=5^2...............
40=2^3*5...........
75=3*5^2\)
LCM = \(2^3*3*5^2=600\)
in choices 9600 is the largest multiple of 6...
_________________
Manager
Manager
avatar
B
Joined: 29 May 2017
Posts: 125
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: The greatest number of four digits which is divisible by 15, 25, 40 an  [#permalink]

Show Tags

New post 29 Oct 2018, 17:17
chetan2u wrote:
Bulusuchaitanya wrote:
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000
B. 9400
C. 9600
D. 9800
E. 9999



the choices straight away give you the answer..
the number has to be multiple of 5 and 2, so has to have 0 as units digit... eliminate E
the number is also a multiple of 3, so the sum of digits of number must be divisible by 3...
9800=9+8+0+0=17.. NOT divisible by 3 so eliminate D
9600 = 9+6+0+0=15...div by 3, so our answer
C

Also the question is basically asking for multiple of the LCM of 15,25,40 and 75
\(15=3*5...........
25=5^2...............
40=2^3*5...........
75=3*5^2\)
LCM = \(2^3*3*5^2=600\)
in choices 9600 is the largest multiple of 6...


I solved this by looking at the GCF ... which is 15 in this case.....
then i looked at each number which was divisible by 15 ... turned out to be C.

I wonder if my logic is correct?
Intern
Intern
avatar
B
Joined: 20 Sep 2018
Posts: 37
Re: The greatest number of four digits which is divisible by 15, 25, 40 an  [#permalink]

Show Tags

New post 29 Oct 2018, 17:42
Bulusuchaitanya wrote:
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000
B. 9400
C. 9600
D. 9800
E. 9999


I would solve this by elimination.

B, D are not multiples of 3 whereas 15, 75 are. So these can be eliminated.

E is odd.

A is too small so I would test 9600 and I see that it is divisible by all.

C it is.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: The greatest number of four digits which is divisible by 15, 25, 40 an  [#permalink]

Show Tags

New post 30 Oct 2018, 19:07
Bulusuchaitanya wrote:
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000
B. 9400
C. 9600
D. 9800
E. 9999


Let’s determine the LCM of 15, 25, 40, and 75:

15 = 3 x 5

25 = 5^2

40 = 2^3 x 5

75 = 5^2 x 3

So the LCM is 2^3 x 3 x 5^2 = 8 x 3 x 25 = 600, and the largest 4-digit number that is a multiple of 600 is 9600.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: The greatest number of four digits which is divisible by 15, 25, 40 an   [#permalink] 30 Oct 2018, 19:07
Display posts from previous: Sort by

The greatest number of four digits which is divisible by 15, 25, 40 an

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne