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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

How many positive integers less than 10,000 are such that the product of their digits is 210? (A) 24 (B) 30 (C) 48 (D) 54 (E) 72

210=1*2*3*5*7=1*6*5*7. (Only 2*3 makes the single digit 6).

So, four digit numbers with combinations of the digits {1,6,5,7} and {2,3,5,7} and three digit numbers with combinations of digits {6,5,7} will have the product of their digits equal to 210.

{1,6,5,7} # of combinations 4!=24 {2,3,5,7} # of combinations 4!=24 {6,5,7} # of combinations 3!=6

Re: How many positive integers less than 10,000 are such that the product [#permalink]

Show Tags

30 Jun 2011, 03:34

1. read question carefully--it says no \(< 10,000\) that means \(10,000 < 4 digit > 999\)and 3 digit \(< 1000\)2. so now 210 has factors \(7,5,3,2,1\)

case 1 : four digit is possible with 7,5,3,2 because multiplication of digit\(=210\) \(4!= 24\) case 2 : we take 3X2=6 and then we can include 1 for four digit no, so no are 7,5,6,1 \(4!=24\)

Quote:

see other muliplication or cases cannot be included because multiplication goes to 2 digit no . ex \(7 X 3 =21\). which is not possible

case 3 : 3 digit no, we can only take 7,6,5 so \(3!=6\) adding all the case \(1,2,3= 54\)that is our answer D. see gmat will not go complicate these kind of question further so all the best
_________________

how many positive integers less than 9999 are such that the product of their digits is 210.

A.24 B.30 C.48 D.56 E.72

Posted from my mobile device

The prime factorization of 210 is 2*3*5*7. So one way to make the right kind of number is to use those four digits, in any of the 4! = 24 orders you can put them in.

Notice though that we can also get 210 as a product by multiplying 5, 6 and 7. So we can make some 3-digit numbers with the right product: 3! = 6 of them to be exact.

But we can also get the right product using the digit 1 along with the digits 5, 6, and 7. Again we can arrange those digits in 4! = 24 orders.

So adding up the possible ways to make the right kinds of number, there are 24+24+6 = 54 ways. I think there might be a typo in your answer choices?
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: How many positive integers less than 10,000 are such that the product [#permalink]

Show Tags

29 Sep 2013, 09:26

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 positive integers less than 10,000 are such that the product [#permalink]

Show Tags

06 Sep 2014, 22:59

cvsmech wrote:

How many positive integers less than 10,000 are such that the product of their digits is 210?

A. 24 B. 30 C. 48 D. 54 E. 72

at first & got no answer for this question by missing the possibility for 3 digit number

prime factor of 210- 2 3 5 7 ... we could make 4! combination using this.. 6(2*3) , 5, 7 , 1 again 4! ... since number could be also three digits 6, 5 ,7 in 3!

how many positive integer less than 10,000 such that product of their digits is 210? ans- 54 how come??

hi anik1989, 210= 2*3*5*7.... now there cannot be any two digits numbers satisfying the condition, as only one set of the numbers (2,3) will give you a single digit... 1) three digits number will consist of 6,5,7.. ways to arrange these three digits = 3!=6.. 2) four digits number will consist of 2,3,5,7 or 1,6,5,7... each will have 4!=24.. TOTAL 24*2=48... TOTAL 1+2=6+48=54... Hope it helped
_________________

Re: How many positive integers less than 10,000 are such that the product [#permalink]

Show Tags

12 Mar 2016, 04:49

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 positive integers less than 10,000 are such that the product [#permalink]

Show Tags

20 Jul 2016, 06:14

I have a question regarding this, I know it will be so basic, but I don't understand why 2x3x5x7x1 is not an option and 6x5x7x1 it is. I mean, why we count 1 in certain options and not in others? Thanks.

Re: How many positive integers less than 10,000 are such that the product [#permalink]

Show Tags

20 Jul 2016, 06:49

I'm sorry but I have to insist. I know that steps, but I don't know the reason why the '1' is not included in the first prime factorisation 2x3x5x7, and we include it in 6x5x7x1, making that different from 6x5x7 (the '1' gives us two different factorisation). I don't know if I explain my request well.

Posted from my mobile device

gmatclubot

Re: How many positive integers less than 10,000 are such that the product
[#permalink]
20 Jul 2016, 06:49

So Africans are the most underrepresented demographic in the top business schools in the world. Why is this so? Well for starters the cost. Paying for an international MBA...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...