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

 It is currently 24 Jun 2018, 18:56

### 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

# How many 4-digit positive integers are multiple of each inte

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

### Hide Tags

Intern
Joined: 09 Mar 2010
Posts: 1
How many 4-digit positive integers are multiple of each inte [#permalink]

### Show Tags

09 Mar 2010, 07:07
2
24
00:00

Difficulty:

(N/A)

Question Stats:

62% (03:01) correct 38% (02:14) wrong based on 68 sessions

### HideShow timer Statistics

How many 4-digit positive integers are multiple of each integer from 1 to 10
Intern
Joined: 09 Mar 2010
Posts: 2
Re: Hi! Math question [#permalink]

### Show Tags

09 Mar 2010, 11:32
2
I am going to assume that you mean 1 to 10 inclusive.

If you wanted to know if a number was divisible by all those digits, you would have to find the smallest # that was divisible by 1 through 10.

1- Every # from 1000 to 9999
1 to 2 - Every even number
1 to 3 - Every multiple of 6 from 1000 to 9999
1 to 4 - Every multiple of 12 from 1000 to 9999
1 to 5 - Every multiple of 60 From 1000 to 9999
1 to 6 - Every multiple of 60 from 1000 to 9999
1 to 7 - Every multiple of 210 from 1000 to 9999
1 to 8 - Every multiple of 840 from 1000 to 9999
1 to 9 - Every multiple of 2520 from 1000 to 9999
1 to 10 - Every multiple of 2520 from 1000 to 9999

With that said, there are three 4-digit numbers that satisfy the requirements of being divisible by 1 through 10 inclusive.
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2657
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: Hi! Math question [#permalink]

### Show Tags

09 Mar 2010, 12:59
didnt get u.....pls elaborate
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Joined: 09 Mar 2010
Posts: 2
Re: Hi! Math question [#permalink]

### Show Tags

09 Mar 2010, 17:33
2
2
If you mean you didn't get my response. Here is the breakdown:

To get a number that is divisible by all 10 numbers you could do 10!. But 10! = 3628800 and it is not the lower common multiple. To get the LCM, I took all the numbers like this:
1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10.
I removed the 6, 8, 9, 10 and added a 3.
I ended up with 1 X 2 X 3 X 3 X 4 X 5 X 7 which equals 2520
I removed the 6 because it is a multiple of 2 and 3 earlier in the list.
I removed the 8 because it is a multiple of 2 and 4 earlier in the list.
I removed the 10 because it is a multiple of 2 and 5 earlier in the list.
For the 9 to be removed, you needed two 3's. So I added a 3 and removed the 9.

With those adjustments I came up with 2520 as the lowest common multiple for integers from 1 to 10.

Because the question asked between the range of 1000 and 9999, three numbers satisfy the requirements: 2520, 5040, 7560.

Finding the lowest common multiple can be a little confusing. I didn't know how to calculate it so I had to work out how to do this on a smaller subset. I used the one through five range to figure how to figure out the LCM.
Math Expert
Joined: 02 Sep 2009
Posts: 46319
Re: Hi! Math question [#permalink]

### Show Tags

10 Mar 2010, 03:06
10
17
lecancher wrote:
Hi,

Can anyone help me with this pls?

how many 4-digit positive integers are multiple of each integer from 1 to 10

4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is $$2^3*3^2*5*7=2520$$.

There are 3 such numbers: 2520, 5040, and 7560.
_________________
Manager
Joined: 09 Dec 2009
Posts: 119
Re: Hi! Math question [#permalink]

### Show Tags

10 Mar 2010, 14:07
gnus wrote:
4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is .

There are 3 such numbers: 2520, 5040, and 7560.
lecancher wrote:
Hi,

Can anyone help me with this pls?

how many 4-digit positive integers are multiple of each integer from 1 to 10

4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is $$2^3*3^2*5*7=2520$$.

There are 3 such numbers: 2520, 5040, and 7560.

Fabulous approach and solution.

Just goes to show that no matter how much you go when you first read a question that there is almost always a shorter route to the answer, if you are clever enough.
_________________

G.T.L. - GMAT, Tanning, Laundry

Round 1: 05/12/10 http://gmatclub.com/forum/handling-a-grenade-thesituation-s-official-debrief-94181.html

Round 2: 07/10/10 - This time it's personal.

Senior Manager
Joined: 21 Jul 2009
Posts: 349
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Re: Hi! Math question [#permalink]

### Show Tags

10 Mar 2010, 19:43
TheSituation wrote:

Fabulous approach and solution.

Just goes to show that no matter how much you go when you first read a question that there is almost always a shorter route to the answer, if you are clever enough.

You nailed the secret to approach GMAT!!! In fact, you are already a Manager. Focus, problem, possibilities and solution, that is all it is in that big bad corporate world. Double Hi Fives bro!!!
_________________

I am AWESOME and it's gonna be LEGENDARY!!!

Manager
Joined: 09 Dec 2009
Posts: 119
Re: Hi! Math question [#permalink]

### Show Tags

11 Mar 2010, 08:18
BarneyStinson wrote:

You nailed the secret to approach GMAT!!! In fact, you are already a Manager. Focus, problem, possibilities and solution, that is all it is in that big bad corporate world. Double Hi Fives bro!!!

Let's meet up at MacLaren's after work for a pint, we can discuss how we gon run dis town after we takeover.
_________________

G.T.L. - GMAT, Tanning, Laundry

Round 1: 05/12/10 http://gmatclub.com/forum/handling-a-grenade-thesituation-s-official-debrief-94181.html

Round 2: 07/10/10 - This time it's personal.

Math Expert
Joined: 02 Sep 2009
Posts: 46319
Re: Hi! Math question [#permalink]

### Show Tags

09 Aug 2010, 03:56
oldstudent wrote:
Bunuel wrote:
lecancher wrote:
Hi,

Can anyone help me with this pls?

how many 4-digit positive integers are multiple of each integer from 1 to 10

4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is $$2^3*3^2*5*7=2520$$.

There are 3 such numbers: 2520, 5040, and 7560.

Hi Bunuel,

Can you please explain how did you get the other 2 nos - 5040 and 7560?

Many thnx

The least 4-digit number which is multiple of each integer from 1 to 10 is LCM of these numbers and equals to $$2^3*3^2*5*7=2520$$.

Now, if we multiply this number by 2 and 3 we will still have 4-digit number which is multiple of each integer from 1 to 10 --> $$2520*2=5040$$ and $$2520*3=7560$$ (if we multiply by 4 the number will be 5-digit). So there are only 3 such numbers.

Hope it's clear.
_________________
Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 645
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: Hi! Math question [#permalink]

### Show Tags

09 Aug 2010, 13:51
Bunuel, awesome answer... Can you please check my post on combinations and answer it when you have a chance.. Thanks

Posted from my mobile device
_________________

Consider kudos, they are good for health

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: How many 4-digit positive integers are multiple of each inte [#permalink]

### Show Tags

05 Mar 2014, 02:18
1
Find LCM of nos between 1 & 10
which also means just LCM of 7,8,9 & 10 (As all smaller are multiple of these)

Just 2 is repeated once, else all are unique

7*8*9*5 = 63*40 = 2520

2520, 2520+2520, 2520+2520+2520 is the answer
_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 18 Nov 2015
Posts: 7
Re: How many 4-digit positive integers are multiple of each inte [#permalink]

### Show Tags

22 May 2016, 07:54
How many 4-digit positive integers are multiple of each integer from 1 to 10

Least No which could be divisible by integers [ 1,2,3,4,5,6,7,8,9,10] is the LCM of the said integers.

LCM [1,2,3,4,5,6,7,8,9,10] = 2520

No the Nos which are divisible by 2520 will be divisible by [1,2,3,4,5,6,7,8,9]

There are 3 values possible between 1000 to 9999

They are 2520 x 1= 2520
2520 x 2 = 5040
2520 x 3 = 7560
Non-Human User
Joined: 09 Sep 2013
Posts: 7058
Re: How many 4-digit positive integers are multiple of each inte [#permalink]

### Show Tags

13 Aug 2017, 08:41
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.
_________________
Re: How many 4-digit positive integers are multiple of each inte   [#permalink] 13 Aug 2017, 08:41
Display posts from previous: Sort by

# How many 4-digit positive integers are multiple of each inte

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

 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®.