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 350,000 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:

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

110 111 271 300 304

any easy way to do this question? here is how i did it... let xyz be a 3-digit#, first, let Z=7, we have 10 options ( 0-9)for x and 10 options for y, then we get 10 x 10 =100, same logic is applied when y =7 and x = 7, we get 300 times. is it correct?

started using the same method, but got stuck in the middle of the road.

Bunuel, could you please clarify if slot method can be applied to this problem. Thanks in advance.

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

110 111 271 300 304

any easy way to do this question? here is how i did it... let xyz be a 3-digit#, first, let Z=7, we have 10 options ( 0-9)for x and 10 options for y, then we get 10 x 10 =100, same logic is applied when y =7 and x = 7, we get 300 times. is it correct?

started using the same method, but got stuck in the middle of the road.

Bunuel, could you please clarify if slot method can be applied to this problem. Thanks in advance.

Re: How many times will the digit 7 be written? [#permalink]
14 Jul 2014, 16:54

1

This post received KUDOS

Alternate solution:

Using probability of occurrence = desired outcomes / total outcomes, desired outcomes = probability x total outcomes.

total outcomes = 1000.

probability of occurrence - to simplify this, the question statement could be interpreted as "what is the probability that the digit 7 is picked at least once when 3 digits are chosen at random?"

probability of at least one 7 = 7 in first digit OR 7 in second digit OR 7 in third digit = 1/10 + 1/10 + 1/10 = 3/10

desired outcomes = probability x total outcomes = 3/10 x 1000 = 300.

Re: How many times will the digit 7 be written? [#permalink]
17 Jul 2014, 21:23

2

This post received KUDOS

The first time I did the question, my answer was C : 271 since I thought the question is "how many numbers from 0 - 1000, that contain the 7 digit". So I counted 77, 707,717,....,777,...797, 771, 772, 773,..., or 779 as one. That may be the reason why 23% of people who answered the question decided to pick answer C. That is really interesting question _________________

......................................................................... +1 Kudos please, if you like my post

Re: How many times will the digit 7 be written? [#permalink]
18 Jul 2014, 13:23

1

This post received KUDOS

vad3tha wrote:

The first time I did the question, my answer was C : 271 since I thought the question is "how many numbers from 0 - 1000, that contain the 7 digit". So I counted 77, 707,717,....,777,...797, 771, 772, 773,..., or 779 as one. That may be the reason why 23% of people who answered the question decided to pick answer C. That is really interesting question

Re: How many times will the digit 7 be written? [#permalink]
11 Dec 2014, 23:30

Bunuel wrote:

nonameee wrote:

Bunuel, can you please explain the logic here? I don't understand it.

Quote:

Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times...

Not sure what can I add to this... It just means that out of 3000 digits we used to write down first 1000 numbers (000, 001, 002, 003, ..., 999), each digit from 0 to 9 is used equal number of times, how else? Thus we used each digit 3000/10=300 times.

HI Bunuel,

I also applied same approach. I got 19 7's per 100. here you have mentioned 20 so why are we counting 77 2 times?

How many times will the digit 7 be written? [#permalink]
27 Mar 2015, 23:39

Another approach: Think of the digits in the form: abcd where a can only be 0 (since 1000 doesn't contain any 7s) and b,c, and d can be any digit from 0-9.

Written Once Ones Place=(1*9*9*1)*1=81 Tens Place= (1*9*1*9)*1=81 Hundreds Place= (1*1*9*9)*1=81

Re: How many times will the digit 7 be written? [#permalink]
30 Mar 2015, 23:26

Let's take numbers from 700 till 799: We have 100 numbers containing 7 as a hundredth digit We have 10 additional 7 if we take the second digit, and 10 more for the units digit Therefore we have 100+10+10=120 7s.

Let's take numbers from 800 till 899: We have 10 numbers with 7 if we take the second digit, and 10 more for the units digit for a total of 20. The same can be applied for the rest of the hundredth which are 8: 000, 100, 200, 300, 400, 500, 600, 900 So in total we have 9*20+120=300

gmatclubot

Re: How many times will the digit 7 be written?
[#permalink]
30 Mar 2015, 23:26

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...

I started running back in 2005. I finally conquered what seemed impossible. Not sure when I would be able to do full marathon, but this will do for now...