GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2018, 18:06

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M09-17

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46129

Show Tags

16 Sep 2014, 00:39
2
4
00:00

Difficulty:

95% (hard)

Question Stats:

41% (01:02) correct 59% (01:08) wrong based on 148 sessions

HideShow timer Statistics

All pages of a book are numbered. If the first page is numbered 1 and the last page is numbered 705, on how many pages does digit 9 appear in the numeration?

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 46129

Show Tags

16 Sep 2014, 00:39
Official Solution:

All pages of a book are numbered. If the first page is numbered 1 and the last page is numbered 705, on how many pages does digit 9 appear in the numeration?

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

Compute on how many pages 9 appears in the first 100 pages and then multiply the result by 7. In the first 100 we have 10 pages where 9 appears as a units digit and 10 pages where 9 appears as a tens digit. Page 99 is counted twice, so the total number of pages on which 9 appears in the first 100 is 19. Therefore, $$19*7 = 133$$.

_________________
Intern
Joined: 22 Oct 2014
Posts: 4
GMAT 1: 740 Q50 V39
GPA: 4
WE: Marketing (Manufacturing)

Show Tags

19 Dec 2014, 00:18
I think that the answer is wrong.
The question is asking on how many pages does number 9 appear and not how many times does number 9 appear.
Therefore page 99 has to be counted once.
Hence correct answer is 18x7= 126
Math Expert
Joined: 02 Sep 2009
Posts: 46129

Show Tags

19 Dec 2014, 08:28
alemazza wrote:
I think that the answer is wrong.
The question is asking on how many pages does number 9 appear and not how many times does number 9 appear.
Therefore page 99 has to be counted once.
Hence correct answer is 18x7= 126

That's not correct.

Pages with 9 in 100: 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99. Total of 19 pages. 19*7 = 133.
_________________
Intern
Joined: 24 Jun 2015
Posts: 46

Show Tags

01 Jul 2015, 08:28
Hi,

If I would like to solve with combinatorics, may be slot method _ x _ x _ ... How the method would proceed?

Thanks a lot.

Best regards.

Luis Navarro
Looking for 700
Manager
Joined: 24 Oct 2013
Posts: 150
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)

Show Tags

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
Math Expert
Joined: 02 Aug 2009
Posts: 5887

Show Tags

14 Mar 2016, 07:15
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Intern
Joined: 16 Feb 2015
Posts: 3
GMAT 1: 710 Q47 V40

Show Tags

06 Jul 2016, 05:17
1
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
Senior Manager
Joined: 31 Mar 2016
Posts: 401
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

Show Tags

29 Jul 2016, 10:47
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi Bunuel,

Can you please take time to explain how this can be done using combination / permutations ?
Manager
Joined: 17 Aug 2015
Posts: 117
GMAT 1: 650 Q49 V29

Show Tags

02 Sep 2016, 10:20
99 NEEDS to be counted as one page as question asks the number of pages on which 9 appears not the total number of 9's
Intern
Joined: 26 May 2016
Posts: 22
GMAT 1: 640 Q49 V30

Show Tags

02 May 2017, 04:25
For those who want to solve this using combinatorics
>> !!!

You do not have the required permissions to view the files attached to this post.

Re: M09-17   [#permalink] 02 May 2017, 04:25
Display posts from previous: Sort by

M09-17

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.