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

 It is currently 15 Nov 2018, 19:28

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

# M01-10

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50613

### Show Tags

24 Dec 2017, 00:37
Siddhuftr wrote:
ones - x - 1 time
tens - x7 + 7x - 9*1 + 1*10 = 19 times
Hundreds - xx7 + x7x + 7xx = 9*10*1 + 9*1*10 + 1*10*10 = 190
Total = 300

I am unable to understand , how double counting of 77 , 777 is avoided ?

The question asks "How many times will the digit 7 be written when listing the integers from 1 to 1000?" not how many number will have 7. So, for example, for number 777, it should be counted as three 7's not one.
_________________
Intern
Joined: 03 Sep 2017
Posts: 15
Location: Brazil
GMAT 1: 730 Q49 V41

### Show Tags

21 May 2018, 08:25
Bunuel wrote:
Official Solution:

How many times will the digit 7 be written when listing the integers from 1 to 1000?

A. 110
B. 111
C. 271
D. 300
E. 304

Many approaches are possible. For example:

Approach #1:

Consider numbers from 0 to 999 written as follows:

1. 000

2. 001

3. 002

4. 003

...

1000. 999

We have 1000 numbers. We used 3 digits per number, hence used total of $$3*1000=3000$$ digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 7) $$\frac{3000}{10}=300$$ times.

Hello Bunuel

Could you kindly explain why did you consider the interval 0 to 999, when the question was about the interval from 1 to 1000?
I understood the ''no favorites'' approach, and i think its a really clever way of solving it. But the interval change got me confused.

Thank you,
Math Expert
Joined: 02 Sep 2009
Posts: 50613

### Show Tags

21 May 2018, 20:28
vitorcbarbieri wrote:
Bunuel wrote:
Official Solution:

How many times will the digit 7 be written when listing the integers from 1 to 1000?

A. 110
B. 111
C. 271
D. 300
E. 304

Many approaches are possible. For example:

Approach #1:

Consider numbers from 0 to 999 written as follows:

1. 000

2. 001

3. 002

4. 003

...

1000. 999

We have 1000 numbers. We used 3 digits per number, hence used total of $$3*1000=3000$$ digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 7) $$\frac{3000}{10}=300$$ times.

Hello Bunuel

Could you kindly explain why did you consider the interval 0 to 999, when the question was about the interval from 1 to 1000?
I understood the ''no favorites'' approach, and i think its a really clever way of solving it. But the interval change got me confused.

Thank you,

Since neither 0 not 1000 has 7 in it, then excluding/including these values into the range won't change the answer.
_________________
Manager
Status: EAT SLEEP GMAT REPEAT!
Joined: 28 Sep 2016
Posts: 170
Location: India

### Show Tags

01 Jun 2018, 07:18
How many times will the digit 7 be written when listing the integers from 1 to 1000?

A. 110
B. 111
C. 271
D. 300
E. 304

Hi Bunuel
Can you please suggest if the below method is correct.

_ _ 7 => 10*10 (since we can use 0 in hundred's place as well in this case)
_ 7 _ => 10*10 (since we can use 0 in hundred's place as well in this case)
7 _ _ => 10*10

Totally = 100+100+100 =300

Option D

Thanks!
_________________

Regards,

Intern
Joined: 01 Aug 2018
Posts: 2

### Show Tags

06 Sep 2018, 04:29
Hello Bunuel

If we look at the approach 1, Doesn't it generalize it for any digit?

Which ever digit you ask for it will come 300 times in 1 to 1000.

Regards,
Amardeep
Intern
Joined: 08 Mar 2018
Posts: 3

### Show Tags

11 Nov 2018, 11:00
approach
For every digit to appear from 1 to 99 -> 20 times any digit will appear
similarly for 100,200,300,400,500,600,800,900 -> total 8*20=160 (Because hundred will remain constant and we know the fact that for 1to99 20 times a digit will appear)
For 700: There will be 100 digits for 7-> 100
For7XX there will be 20 ways ->20
Total (20+160+100+20) there will be 300 digits

I hope it helps a bit. Press Kudos :P
M01-10 &nbs [#permalink] 11 Nov 2018, 11:00

Go to page   Previous    1   2   3   [ 46 posts ]

Display posts from previous: Sort by

# M01-10

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®.