NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 03:19 It is currently 26 Apr 2024, 03:19
Decision Tracker
My Rewards
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

M09-17

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619101 [11]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
M09-17 [#permalink] New post   16 Sep 2014, 00:39
2
Kudos
9
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

55% (01:48) correct 45% (02:03) wrong based on 117 sessions
Hide Show timer Statistics
In a book with numbered pages, the first page is numbered 1 and the last page is numbered 705. On how many pages does the digit 9 appear in the page numbering?

A. 70
B. 77
C. 126
D. 133
E. 140
ShowHide Answer
Official Answer
D
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619101 [4]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re M09-17 [#permalink] New post   16 Sep 2014, 00:39
4
Bookmarks
Expert Reply
Official Solution:

In a book with numbered pages, the first page is numbered 1 and the last page is numbered 705. On how many pages does the digit 9 appear in the page numbering?

A. 70
B. 77
C. 126
D. 133
E. 140


To calculate how many pages feature the digit 9 in the page numbering, first determine how many times 9 appears in the first 100 pages, and then multiply that result by 7, as there are 7 blocks of 100 numbers (1-100, 101-200, ..., 601-700). In the first 100 pages, there are 10 pages where 9 appears as a units digit (9, 19, 29, ..., 99) and 10 pages where 9 appears as a tens digit (90, 91, 92, ..., 99). Page 99 is counted twice, so the total number of pages on which 9 appears in the first 100 is 19. Therefore, there are \(19 * 7 = 133\) pages with the digit 9 in the page numbering.


Answer: D
User avatar
S
deepthit
Manager
Manager
Joined: 24 Oct 2013
Posts: 108
Own Kudos [?]: 58 [0]
Given Kudos: 129
Location: India
Concentration: General Management, Strategy
WE:Information Technology (Computer Software)
Send PM
Re: M09-17 [#permalink] New post   14 Mar 2016, 07:09
Here are the list of numbers
9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99
Total - 20 9's in 1 hundred. Total = 20*7 = 140
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11179
Own Kudos [?]: 31938 [1]
Given Kudos: 290
Send PM
Reviews Badge
Re: M09-17 [#permalink] New post   14 Mar 2016, 07:15
1
Bookmarks
Expert Reply
deepthit wrote:
Here are the list of numbers
9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99
Total - 20 9's in 1 hundred. Total = 20*7 = 140


the Q ask us about the PAGES on which 9 occurs, so 99 will be ONE and not two separately
so 19*7
avatar
chickxxchococat
Intern
Intern
Joined: 16 Feb 2015
Posts: 1
Own Kudos [?]: 3 [3]
Given Kudos: 3
Schools: Kelley '18 Tepper '18
GMAT 1: 710 Q47 V40
Send PM
Reviews Badge
Re: M09-17 [#permalink] New post   06 Jul 2016, 05:17
3
Kudos
Another approach:

Pages from 1 to 705.

9 as units digit: 9- first number in set, 699-last number in set, set is inclusive. Distance between each occurrence of '9' in units digits = 10.
>> Number of occurrences = [(699-9)/10] + 1 = 70

9 as tenths digit: if hundredth digit is '0', we have 90-first number in set, 98-last number in set (omit 99 as already counted above), set is inclusive.
>> Number of occurrences: (98-90) + 1 = 9
Possible hundredth digits: 0 1 2 3 4 5 6 >> total number of occurrences = 9*7=63

Finally: total pages with '9' = 63 +70 = 133
avatar
B
manojach87
Intern
Intern
Joined: 26 May 2016
Posts: 13
Own Kudos [?]: 34 [2]
Given Kudos: 5
GMAT 1: 640 Q49 V30
Send PM
Re: M09-17 [#permalink] New post   02 May 2017, 04:25
1
Kudos
1
Bookmarks
For those who want to solve this using combinatorics
Attachments

solving with combinatorics.png
solving with combinatorics.png [ 45.73 KiB | Viewed 21157 times ]

User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619101 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: M09-17 [#permalink] New post   08 May 2023, 08:59
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
GMAT Club Bot
gmatclubot
Re: M09-17 [#permalink]
08 May 2023, 08:59
Moderator:
Bunuel
Math Expert
92929 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions