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:

Explanation from the book makes more sense now that I've thought about it a bit more.

Let ABCD be your four digits; D has to be odd since the four-digit number is odd (5 odd digits from the sequence). A has 8 options (1 thru 9, but one of the unit is reserved for digit D); B has 8 options aswell (0 thru 9, again one digit is reserved for digit D); C has 7 options (0 thru 9; one digit accounted for D and two A and B); D has 5 options since it must be odd.

8*8*7*5 = 2240

What threw me off was my assumtion that all four digits must be odd, but for a number to be odd only the last digit has to be odd. Hope this helps.

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

09 Jun 2009, 10:05

Answer should be D.

Let a 4-digit number be represented by ABCD

Here A can have any value between 1 to 9 - so total 9 B can have any value between 0 to 9, but not A - so total 9 C can have any value between 0 to 9, but not A or B - so total 8 D can have any value between 0 to 9, but not A, B or C - so total 7

No. of ALL possible 4-digit nos (without repeating any digit) = 9*9*8*7 = 4536 Half of these would be odd. Therefor, no. of ODD possible 4-digit nos (without repeating any digit) = 4536 / 2 = 2268 _________________

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

09 Jun 2009, 17:00

1

This post received KUDOS

Thank you all who responded.

The answer is C, 2240.

Explanation from the book makes more sense now that I've thought about it a bit more.

Let ABCD be your four digits; D has to be odd since the four-digit number is odd (5 odd digits from the sequence). A has 8 options (1 thru 9, but one of the unit is reserved for digit D); B has 8 options aswell (0 thru 9, again one digit is reserved for digit D); C has 7 options (0 thru 9; one digit accounted for D and two A and B); D has 5 options since it must be odd.

8*8*7*5 = 2240

What threw me off was my assumtion that all four digits must be odd, but for a number to be odd only the last digit has to be odd. Hope this helps.

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

09 Jun 2009, 22:45

1

This post received KUDOS

This question has to be solved reverse ABCD is a 4 digit number

Since D (the unit digit) has to be odd, we have 5 choices => D=5 Starting from A; A can hold 1 to 9, but cannot contain the digit in unit position, so choices will be 8 => A = 8 B can gold 0 to 9 (10 choices), but not the digits in A and D, so we ahve 8 options => B = 8 C can also hold 0 to 9 (10 choices), but not the digits in A, B and D, se we have 7 choices => C = 7

Calculating the total number of options = A*B*C*D = 8*8*7*5 = 2240

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

10 Jun 2009, 07:17

I wonder as to why shud i not solve it the other around...

tha last digit can have 5 ways. the second last digit can have 9 ways. ( 0-9) except the last digit. the third last digit cab have 8 ways ( 0-9) except the last and the second last digit. the fourth last digit can have 6 ways ( as no zero, last digiht, second last, thirdt last)

hence the total will be 45*48 = 2160 ways..

can anyone tell me from where am i missing the extra 80 ways..

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

10 Jun 2009, 09:33

Expert's post

Neochronic wrote:

I wonder as to why shud i not solve it the other around...

tha last digit can have 5 ways. the second last digit can have 9 ways. ( 0-9) except the last digit. the third last digit cab have 8 ways ( 0-9) except the last and the second last digit. the fourth last digit can have 6 ways ( as no zero, last digiht, second last, thirdt last)

hence the total will be 45*48 = 2160 ways..

can anyone tell me from where am i missing the extra 80 ways..

The highlighted part is correct only if second, third and fourth digits don't equal zero. Otherwise, we will have 7 ways. _________________

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

05 Jan 2011, 08:21

EnergySP wrote:

Thank you all who responded.

The answer is C, 2240.

Explanation from the book makes more sense now that I've thought about it a bit more.

Let ABCD be your four digits; D has to be odd since the four-digit number is odd (5 odd digits from the sequence). A has 8 options (1 thru 9, but one of the unit is reserved for digit D); B has 8 options aswell (0 thru 9, again one digit is reserved for digit D); C has 7 options (0 thru 9; one digit accounted for D and two A and B); D has 5 options since it must be odd.

8*8*7*5 = 2240

What threw me off was my assumtion that all four digits must be odd, but for a number to be odd only the last digit has to be odd. Hope this helps.

I know it is an old post but I received 2160 as an answer and can´t figure out which one is correct.

I start from the last digit: 5 possiblities for the last digit 9 possibilities or the 3rd digit 8 for the 2nd and 6 for the 1st

So we have 6*8*9*5=2160

But EnergySP solution is also correct. Now I am confused. Can somebody help?

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

05 Jan 2011, 10:06

Expert's post

medanova wrote:

EnergySP wrote:

Thank you all who responded.

The answer is C, 2240.

Explanation from the book makes more sense now that I've thought about it a bit more.

Let ABCD be your four digits; D has to be odd since the four-digit number is odd (5 odd digits from the sequence). A has 8 options (1 thru 9, but one of the unit is reserved for digit D); B has 8 options aswell (0 thru 9, again one digit is reserved for digit D); C has 7 options (0 thru 9; one digit accounted for D and two A and B); D has 5 options since it must be odd.

8*8*7*5 = 2240

What threw me off was my assumtion that all four digits must be odd, but for a number to be odd only the last digit has to be odd. Hope this helps.

I know it is an old post but I received 2160 as an answer and can´t figure out which one is correct.

I start from the last digit: 5 possiblities for the last digit 9 possibilities or the 3rd digit 8 for the 2nd and 6 for the 1st

So we have 6*8*9*5=2160

But EnergySP solution is also correct. Now I am confused. Can somebody help?

See Walker's post above: you'll have 6 choices for the 1st digit if 2nd or 3rd digit doesn't equal to zero, otherwise you'll have 7 choices. So this approach is not correct. _________________

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

05 Jan 2011, 12:34

four Digit Number which is odd i.e it must end with 1,3,5,7 or 9

So if following 4 blanks represent the 4 digit number:

- - - -

Unit's place can be filled in by any of the 5 digits (1,3,5,7 or9)

so we get,

- - - 5

We are left with 9 other numbers to fill in the rest, but we cannot repeat and first digit cannot be zero otherwise the number will not be truly 4 digit number.

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

01 Jun 2011, 08:07

Why can't we approach from the first number

1. Cannot be "0", hence number of options - 9 2. Leaving the number in 1st place, gives options - 9 again 3. Leaving the number in 1st/ 2nd place, gives options - 8 4. Last has to be an ODD number, so options -5

So numbers possible = 9X9X8X5 =3240 we do not have any options so the answer is definitely WRONG. Is it because the number of options that i am putting for last digit "5" is incorrect because some of them may have already been used up in 1/2/3 rd places.

So what should be the GENERIC order to giving the number of options possible in such problems?

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

01 Jun 2011, 08:25

2

This post received KUDOS

1

This post was BOOKMARKED

CyberAsh wrote:

Why can't we approach from the first number

1. Cannot be "0", hence number of options - 9 2. Leaving the number in 1st place, gives options - 9 again 3. Leaving the number in 1st/ 2nd place, gives options - 8 4. Last has to be an ODD number, so options -5

So numbers possible = 9X9X8X5 =3240 we do not have any options so the answer is definitely WRONG. Is it because the number of options that i am putting for last digit "5" is incorrect because some of them may have already been used up in 1/2/3 rd places.

So what should be the GENERIC order to giving the number of options possible in such problems?

I think you should look for something called "Slot Method" in MGMAT guide for P&C.

The idea is to assign the number in ascending order of restriction.

Units place: 1,3,5,7,9- Total=5(Most restrictive) Thousands place: No 0 and not the digit used by units place- Total=8 (Less restrictive) Tens place: 2 digits used. Left:10-2=8 (Yet less restrictive) Hundreds place: 3 digits used. Left:10-3=7(Yet less restrictive)

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

01 Jun 2011, 16:42

fluke wrote:

CyberAsh wrote:

Why can't we approach from the first number

1. Cannot be "0", hence number of options - 9 2. Leaving the number in 1st place, gives options - 9 again 3. Leaving the number in 1st/ 2nd place, gives options - 8 4. Last has to be an ODD number, so options -5

So numbers possible = 9X9X8X5 =3240 we do not have any options so the answer is definitely WRONG. Is it because the number of options that i am putting for last digit "5" is incorrect because some of them may have already been used up in 1/2/3 rd places.

So what should be the GENERIC order to giving the number of options possible in such problems?

I think you should look for something called "Slot Method" in MGMAT guide for P&C.

The idea is to assign the number in ascending order of restriction.

Units place: 1,3,5,7,9- Total=5(Most restrictive) Thousands place: No 0 and not the digit used by units place- Total=8 (Less restrictive) Tens place: 2 digits used. Left:10-2=8 (Yet less restrictive) Hundreds place: 3 digits used. Left:10-3=7(Yet less restrictive)

Re: How many four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

27 Oct 2014, 08:47

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 four-digit odd numbers do not use any digit more than once? [#permalink]

Show Tags

05 Nov 2015, 12:56

Just curious how do you know where the option for zero can be counted as well? i.e hundreds vs thousands? I would assume that as long as it is not counted in the unit digits it's all that matters.

It's quite clear to me why not the digits because then for example 7530 becomes divisible by 2. But what difference does 7053 and 7503 make?

Thank you!

gmatclubot

Re: How many four-digit odd numbers do not use any digit more than once?
[#permalink]
05 Nov 2015, 12:56

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...