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 350,000 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:

Re: Number Properties Problem [#permalink]
24 Aug 2010, 07:08

1

This post received KUDOS

seekmba wrote:

can someone please explain this in detail?

hi seek This is a basic structure of any multiplication principle : I will put it down ; if an event can occur in " m " diffeent ways and if following it a second event can occur in " n "diferent ways , then two events in succession can occur in m X n ways ....

e.g in a cinema there are 3 entrance door and 2 exit doors ..then a person can have 3 * 2 = 6 possible routes ....

I have taken this explantion from the introduction of Permutation topic . If you want more help I can scan a few pages from a book which has about 10 -15 question and answers on this topic ...

similar question can be how many 3 digit odd numbers can be formed by using the digits 1 2 3 4 5 6 such that there is no repetition ....

Re: Number Properties Problem [#permalink]
24 Aug 2010, 08:49

1

This post received KUDOS

1

This post was BOOKMARKED

I have been trying to solve the question with the digits not being repeated. This is how it goes: Case 1: One Digit Number: 4 ways Case 2: Two Digits Numbers: 4*3 = 12 ways Case 3: Three Digits Numbers: 3*3*2 = 18 ways Therefore, total number of ways = 4+12+18= 34. Am I correct? I think I am and therefore I was wondering how the answer could be 60 when the digits are not repeated.

In case the digits are repeated: Case 1: One Digit Numbers: 4 ways Case 2: Two Digits Numbers: 4*4 = 16 ways Case 3: Three Digits Numbers: 3*4*4 = 48 ways Therefore, total number of ways = 4+16+48 = 68.

Last edited by shekharvineet on 24 Aug 2010, 08:55, edited 1 time in total.

Re: Number Properties Problem [#permalink]
24 Aug 2010, 09:03

1

This post received KUDOS

seekmba wrote:

can someone please explain this in detail?

Hi. Here it goes. In case the digits are repeated: Case 1: One Digit Numbers: It can be filled by any of those four numbers in 4 different ways. Case 2: Two Digits Numbers: The tens' place can be filled by those four numbers in 4 different ways. Similarly the units' place can be filled in 4 different ways, since the numbers can be repeated. So, number of ways of filling two digits numbers = 4*4 = 16. Case 3: Now there is a restriction here. We are to find positive integers less that 500, so 5 caanot be used to fill up the hundreds' place. It can be filled in only 3 different ways. But the tens' place and units' place each can be filled in 4 different ways. So, number of ways of filling three digitd numbers= 3*4*4 = 48. Hence, total number of ways = 4+16+48 = 68.

Re: Number Properties Problem [#permalink]
30 Aug 2010, 12:33

Divyababu wrote:

if the digits are not repeated then it is 52 ways

_ 4 ways _ _ 4*3 ways _ _ _ (1st digit cant take 5 as it should be less than 500 so it 3 ways )3*4*3 4+12+36=52

if it is repeated than it is 68 ways

_ 4 ways

_ _ 4*4 ways =16

_ _ _ 3*4*4=48

48+16+4=68

I don't think your answer is correct when the digits are not repeated. That is , the correct answer is 34 and not 52.

Now we agree that in case of One digit numbers, it can be filled in 4 ways; and in case of two digit numbers, it can be filled in 4*3= 12 ways. But I beg to differ when it comes to three digit numbers. I say that 5 cannot be used to fill the hundreds place because there is a restriction that the number has to less than 500. How can you even allow 5 to fill the hundreds place because the question clearly says it has be less than 500, i.e till 499. Even if we change the question and ask to find the number of ways the digits 1, 2, 3 and 5 can be used to form numbers less than or equal to 500, and allow 5 to occupy the hundreds place, how will you fill up the remaining two places, i.e. the tens place and the units place because the other three digits are 1, 2 and 3 which are all greater than 0. So if you allow 5 to fill the hundreds place, it voilates the entire question. So, there are only 3*3*2 = 18 ways of filling in case of three digit numbers.

Re: Number Properties Problem [#permalink]
17 Jan 2014, 07:19

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 500 can be formed using [#permalink]
29 Sep 2014, 04:54

Expert's post

1

This post was BOOKMARKED

him1985 wrote:

Bunuel wrote:

Temurkhon wrote:

In this case to include 500 we need zeroes as possible digits but we do not have them, so there is no difference between <500 and <501. Is that right?

Yes, that's correct.

Hi Bunuel,

I could not get the logic behind this. Can you please explain? Is there any other easy way to solve such questions?

How many positive integers less than 500 can be formed using the numbers 1, 2, 3 and 5 for the digits?

(A) 48 (B) 52 (C) 66 (D) 68 (E) 84

Positive integers less than 500 can be:

1. A single-digit integer: 4 2. A double-digit integer: 4*4. 3. A three-digit integer: 3*4*4 (the hundreds digit cannot be 5, so we have only 3 options for it).

Michigan Ross: Center for Social Impact : The Center for Social Impact provides leaders with practical skills and insight to tackle complex social challenges and catalyze a career in...

The Importance of Financial Regulation : Before immersing in the technical details of valuing stocks, bonds, derivatives and companies, I always told my students that the financial system is...

The following pictures perfectly describe what I’ve been up to these days. MBA is an extremely valuable tool in your career, no doubt, just that it is also...