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 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576 B. 520 C. 504 D. 432 E. 348

A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive). 8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit). 8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

06 Sep 2013, 00:59

Bunuel wrote:

aparnaharish wrote:

How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576 B. 520 C. 504 D. 432 E. 348

A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive). 8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit). 8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

9*8*8=576.

Answer: A.

Hi Bunuel,

why is this solution wrong? 9C1 options for the first digit (from 1 to 9 inclusive). 9C1 options for the Second digit (from 0 to 9 inclusive minus the one we used for the first digit). 7C1 options for the third digit (from 1 to 9 inclusive minus 2 digits we used for the first and the second digits)

How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576 B. 520 C. 504 D. 432 E. 348

A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive). 8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit). 8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

9*8*8=576.

Answer: A.

Hi Bunuel,

why is this solution wrong? 9C1 options for the first digit (from 1 to 9 inclusive). 9C1 options for the Second digit (from 0 to 9 inclusive minus the one we used for the first digit). 7C1 options for the third digit (from 1 to 9 inclusive minus 2 digits we used for the first and the second digits)

Which gives 9*9*7=567

Where i am wrong???

Thanks in Advance, Rrsnathan.

If the second digit is 0, then you'll have 8 not 7 options for the third digit.

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

06 Sep 2013, 10:21

Bunuel wrote:

aparnaharish wrote:

How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576 B. 520 C. 504 D. 432 E. 348

A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive). 8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit). 8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

9*8*8=576.

Answer: A.

Hi Bunuel,

why is this solution wrong? 9C1 options for the first digit (from 1 to 9 inclusive). 9C1 options for the Second digit (from 0 to 9 inclusive minus the one we used for the first digit). 7C1 options for the third digit (from 1 to 9 inclusive minus 2 digits we used for the first and the second digits)

Which gives 9*9*7=567

Where i am wrong???

Thanks in Advance, Rrsnathan.

If the second digit is 0, then you'll have 8 not 7 options for the third digit.

Hope it's clear.

It will still be wrong it is 9*9*8 and not 9*8*8... still confused

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

05 Dec 2014, 19:01

Bunuel, Why must one go by 1st-3rd-2nd digit option and not 1st-2nd-3rd digit option, which would result in 9*9*8?

Bunuel wrote:

aparnaharish wrote:

How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576 B. 520 C. 504 D. 432 E. 348

A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive). 8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit). 8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

06 Dec 2014, 12:05

Amit0507 wrote:

Bunuel, Why must one go by 1st-3rd-2nd digit option and not 1st-2nd-3rd digit option, which would result in 9*9*8?

hi, there can be certain cases in which zero can occur at the 3rd digit, if one follows 1st-2nd-3rd digit option. in order to eliminate all such cases we go with 1st-3rd-2nd digit option.

remember a number will be divisible by 10 if its last digit ends with zero, and in this case we want to eliminate all such cases in which zero occurs at the unit digit.

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

06 Dec 2014, 18:06

Hi Manpreet, The approach is still not clear to me. By 9*9*8 option, we eliminate the possibility of a Zero at the 3rd place.

manpreetsingh86 wrote:

Amit0507 wrote:

Bunuel, Why must one go by 1st-3rd-2nd digit option and not 1st-2nd-3rd digit option, which would result in 9*9*8?

hi, there can be certain cases in which zero can occur at the 3rd digit, if one follows 1st-2nd-3rd digit option. in order to eliminate all such cases we go with 1st-3rd-2nd digit option.

remember a number will be divisible by 10 if its last digit ends with zero, and in this case we want to eliminate all such cases in which zero occurs at the unit digit.

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

07 Dec 2014, 01:57

Amit0507 wrote:

Hi Manpreet, The approach is still not clear to me. By 9*9*8 option, we eliminate the possibility of a Zero at the 3rd place.

lets try to understand, why we approach this question from first digit and why not from second or third digit ??

we don't want zero at the first digit. why ?? if zero occurs at the first digit then number won't be a three digit number(it will become a two digit number). that's why we want to eliminate all such cases in which zero occurs at the first digit so we started with first digit. now up to this point we have 9 possibilities for first digit . which are 1,2,3,4,5,6,7,8,9. suppose we selected 9 for the first digit. so number will be 9,_,_

now lets suppose we follow your method. so for second digit we have 0,1,2,3,4,5,6,7,8. now from these 9 numbers suppose we selected digit 8

so the number is 98_

now for third digit we have 0,1,2,3,4,5,6,7, now from these 8 number we can select any of the number. that is we have certain cases in which 0 can also occur at the third digit. (i.e. 980 is one of the possible number) which we don't want.

hence we have to eliminate all such possible cases.

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

07 Dec 2014, 02:44

You mixed possibilities with the number at the highlighted section. Let me explain my approach. 1. I have 9 possibilities for the 1st digit. 2. I have again 9 possibilities for the second place as I will consider 0 here 3. Now out of 10, 2 numbers are used. If I assume 0 was used in the second place (10_) then I have 8 possibilities for the last place as well. so the final possibility will be 9*9*8. I hope I made myself clear on the understanding. Please point out the flaw.

manpreetsingh86 wrote:

Amit0507 wrote:

Hi Manpreet, The approach is still not clear to me. By 9*9*8 option, we eliminate the possibility of a Zero at the 3rd place.

lets try to understand, why we approach this question from first digit and why not from second or third digit ??

we don't want zero at the first digit. why ?? if zero occurs at the first digit then number won't be a three digit number(it will become a two digit number). that's why we want to eliminate all such cases in which zero occurs at the first digit so we started with first digit. now up to this point we have 9 possibilities for first digit . which are 1,2,3,4,5,6,7,8,9. suppose we selected 9 for the first digit. so number will be 9,_,_

now lets suppose we follow your method. so for second digit we have 0,1,2,3,4,5,6,7,8. now from these 9 numbers suppose we selected digit 8

so the number is 98_

now for third digit we have 0,1,2,3,4,5,6,7, now from these 8 number we can select any of the number. that is we have certain cases in which 0 can also occur at the third digit. (i.e. 980 is one of the possible number) which we don't want.

hence we have to eliminate all such possible cases.

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

07 Dec 2014, 02:57

Amit0507 wrote:

You mixed possibilities with the number at the highlighted section. Let me explain my approach. 1. I have 9 possibilities for the 1st digit. 2. I have again 9 possibilities for the second place as I will consider 0 here 3. Now out of 10, 2 numbers are used. If I assume 0 was used in the second place (10_) then I have 8 possibilities for the last place as well. so the final possibility will be 9*9*8. I hope I made myself clear on the understanding. Please point out the flaw.

manpreetsingh86 wrote:

Amit0507 wrote:

Hi Manpreet, The approach is still not clear to me. By 9*9*8 option, we eliminate the possibility of a Zero at the 3rd place.

lets try to understand, why we approach this question from first digit and why not from second or third digit ??

we don't want zero at the first digit. why ?? if zero occurs at the first digit then number won't be a three digit number(it will become a two digit number). that's why we want to eliminate all such cases in which zero occurs at the first digit so we started with first digit. now up to this point we have 9 possibilities for first digit . which are 1,2,3,4,5,6,7,8,9. suppose we selected 9 for the first digit. so number will be 9,_,_

now lets suppose we follow your method. so for second digit we have 0,1,2,3,4,5,6,7,8. now from these 9 numbers suppose we selected digit 8

so the number is 98_

now for third digit we have 0,1,2,3,4,5,6,7, now from these 8 number we can select any of the number. that is we have certain cases in which 0 can also occur at the third digit. (i.e. 980 is one of the possible number) which we don't want.

hence we have to eliminate all such possible cases.

how do you know that zero will be at the second position. ?? i have highlighted one of the cases in which zero will not be at the second position.

and my dear friend, i'm not mixing any possibilities. that's the correct way of approaching the problem.

Re: How many 3 digit positive integers with distinct digits [#permalink]

Show Tags

07 Feb 2016, 09:57

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.
_________________

How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576 B. 520 C. 504 D. 432 E. 348

Let’s analyze the number of choices for each of the 3 digits from left to right.

Since the first digit can’t be 0, there are 9 choices for the first digit.

Since the second digit can’t be same as the first digit (but it can be 0), there are also 9 choices for the second digit. However, let’s consider the following two cases: 1) the second digit is not 0, and 2) the second digit is 0. For each of these two cases, we will also consider the last digit.

Case 1: The second digit is not 0

Since the second digit is not 0 (and it can’t be the same as the first digit), there are 8 choices for the second digit. As for the last digit, it can’t be 0 (otherwise it will be a multiple of 10) and it can’t be the same as either of the first two digits; thus, there are 7 choices. Thus, there are 9 x 8 x 7 = 504 three-digit numbers with distinct digits when the second digit is not 0.

Case 2: The second digit is 0

Since the second digit is 0, there is only 1 choice for the second digit. As for the last digit, it can’t be 0 (otherwise it will be a multiple of 10) and it can’t be the same as either of the first two digits. However, since the last digit won’t be 0, it won’t be the same as the second digit. In other words, it only needs to be different from the first digit; thus there are 8 choices. Thus, there are 9 x 1 x 8 = 72 three-digit numbers with distinct digits when the second digit is 0.

Lastly, the number of three-digit numbers with distinct digits is 504 + 72 = 576.

Answer: A
_________________

Scott Woodbury-Stewart Founder and CEO

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

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

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...