Last visit was: 05 Jun 2024, 20:05 It is currently 05 Jun 2024, 20:05
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

How many numbers between 10,000 and 40,000 which **do not**

User avatar
Praetorian
CEO
CEO
Joined: 15 Aug 2003
Posts: 2876
Own Kudos [?]: 1651 [0]
Given Kudos: 781
Send PM
How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   06 Dec 2003, 16:27
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
4.How many numbers between 10,000 and 40,000 which **do not** contain the digits 7 and 4 , can be divided by 15 ?



5.How many numbers between 10,000 and 100,000 **do not** have
reapeting digits and the the digits 3, 4 and 5 appear in ascending order(*but not necessarily adjacent*) ?



any NON - brute force ideas?

thanks



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
BG
Senior Manager
Senior Manager
Joined: 13 Nov 2003
Posts: 356
Own Kudos [?]: 178 [0]
Given Kudos: 0
Location: BULGARIA
Concentration: INSURANCE, RISK MANAGEMENT
 Q49  V38
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   07 Dec 2003, 06:28
for Q1. Numbers without 7 AND 4 we can have are 3x8x8x8x8=12 288 , numbers divisible by 15 should end with 5 OR 0, and the sum of numbers is divisible by 3, 10005,10010, 10015,10020,10025,10030,10035 so every third number is divisible by 15 or we have 12 288/3=4096...IMO :)
User avatar
Praetorian
CEO
CEO
Joined: 15 Aug 2003
Posts: 2876
Own Kudos [?]: 1651 [0]
Given Kudos: 781
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   07 Dec 2003, 07:01
BG wrote:
for Q1. Numbers without 7 AND 4 we can have are 3x8x8x8x8=12 288 , numbers divisible by 15 should end with 5 OR 0, and the sum of numbers is divisible by 3, 10005,10010, 10015,10020,10025,10030,10035 so every third number is divisible by 15 or we have 12 288/3=4096...IMO :)



need more help with => 3x8x8x8x8=12 288
User avatar
BG
Senior Manager
Senior Manager
Joined: 13 Nov 2003
Posts: 356
Own Kudos [?]: 178 [0]
Given Kudos: 0
Location: BULGARIA
Concentration: INSURANCE, RISK MANAGEMENT
 Q49  V38
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   07 Dec 2003, 07:10
Since your number is between 10000 and 40000 first number we can select in 3 ways (1,2,3) the rest in 8 ways each ( without 7 and 4) which is ultimately 3x8x8x8x8
User avatar
Praetorian
CEO
CEO
Joined: 15 Aug 2003
Posts: 2876
Own Kudos [?]: 1651 [0]
Given Kudos: 781
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   07 Dec 2003, 07:11
BG wrote:
Since your number is between 10000 and 40000 first number we can select in 3 ways (1,2,3) the rest in 8 ways each ( without 7 and 4) which is ultimately 3x8x8x8x8



Wanna check your solution?

hint : the last digit can be only 5 or 0.

praetorian
User avatar
Praetorian
CEO
CEO
Joined: 15 Aug 2003
Posts: 2876
Own Kudos [?]: 1651 [0]
Given Kudos: 781
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   08 Dec 2003, 03:16
BG wrote:
is it 3072?


well ,3072/3 would be your "current" solution.

i am worried about your criteria for divisiblity ...

every third # divisible by 15??

are you sure it works for all the #'s

thanks
praetorian
User avatar
bat_car
Intern
Intern
Joined: 04 Oct 2003
Posts: 25
Own Kudos [?]: 3 [0]
Given Kudos: 0
Location: Silicon Valley, CA
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   Updated on: 21 Dec 2003, 10:11
Q1.
Total No's are 3*8*8*8*2. For divisibility by 15, the Nos are
10,005, 10020, 10035 ... etc; so these are 15 appart. In this seris there will be no numbers with 7 or 4 as the digits. so we have 30,000/15 = 2,000 numbers.

It seesm that the first part about digits is redundant information. Is this solution correct. :roll:

Originally posted by bat_car on 09 Dec 2003, 02:28.
Last edited by bat_car on 21 Dec 2003, 10:11, edited 1 time in total.
User avatar
BG
Senior Manager
Senior Manager
Joined: 13 Nov 2003
Posts: 356
Own Kudos [?]: 178 [0]
Given Kudos: 0
Location: BULGARIA
Concentration: INSURANCE, RISK MANAGEMENT
 Q49  V38
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   09 Dec 2003, 04:09
345XX as a pair XX can occupy 4 places in 3 of them we have 42 possibilities when is at the beginning only 36 possibilities( without 0)3x42=126+36=162 different numbers, when separate 12 ways of ordering the two numbers but in 6 of them it can not be 0 or 6x36+6x42=216+252=468, total 162+468=630 numbers.. :)
User avatar
bat_car
Intern
Intern
Joined: 04 Oct 2003
Posts: 25
Own Kudos [?]: 3 [0]
Given Kudos: 0
Location: Silicon Valley, CA
Send PM
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink] How many numbers between 10,000 and 40,000 which **do not**   21 Dec 2003, 10:24
praetorian123 could you please post the correct Ans.
Thanks



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: How many numbers between 10,000 and 40,000 which **do not** [#permalink]
21 Dec 2003, 10:24
Moderators:
Bunuel
Math Expert
93527 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3131 posts