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.

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 [#permalink]
12 Jul 2010, 20:12

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

What is the best approach to solve problems such as these two examples below. If someone can solve them and show me the steps they took, I would appreciate it greatly. The GMAT Club test explanations were a little difficult for me to digest.

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

"How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?"

Re: Digits Problem Difficulty in GMAT Club test 1 [#permalink]
12 Jul 2010, 20:59

6

This post received KUDOS

Expert's post

tonebeeze wrote:

What is the best approach to solve problems such as these two examples below. If someone can solve them and show me the steps they took, I would appreciate it greatly. The GMAT Club test explanations were a little difficult for me to digest.

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

"How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?"

Answer: 1339

Thanks Club!

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

Many approaches are possible. For example:

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) 3000/10=300 times.

Answer: 300.

2. How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?

There is one number in hundred with 2 in th tens digit and 1 in the units digit: 21, 121, 221, 321, ...

The difference between 324,700 and 458,600 is 458,600-324,700=133,900 - one number per each hundred gives 133,900/100=1,339 numbers.

Re: Digits Problem Difficulty in GMAT Club test 1 [#permalink]
14 Jul 2010, 20:57

1

This post received KUDOS

When we write the numbers 1 to 1000 do we use 3 digits for each number?

What about: 0 1 2 3 4 5 6 7 8 9

and

10...99

The reason it works out is because we don't use zero later

so you could think of 1 as 001 and 10 as 010

However, if the question changed to how many 7's from 100 to 1000.

Then you have 900 numbers with 3 digits = 3*900 = 2700 total digits

2700 / 10 = 270

when we actually have 280 7's from 100 to 1000. right?

I came up with the same answer for the posted question 300, by counting the 7's in different groups

1 to 9= Only one 7 (7) 10 to 99= 19 (17,27,37,47,57,67,87,97 and 70, 71, 72, 73, 74, 75, 76, 78, 79 and 77 (2 sevens)) then I knew from 100 to 1000 these 20 sevens would repeat 9 more times plus all the 7's in the hundreds digits 100 sevens from 700 to 799

1 (7) +19 (tens and ones digits from 10 to 99) +180 (tens and ones digits from 100 to 1000) +100 (hundreds digits) =300

Re: Digits Problem Difficulty in GMAT Club test 1 [#permalink]
15 Jul 2010, 07:26

1

This post received KUDOS

Expert's post

TallJTinChina wrote:

When we write the numbers 1 to 1000 do we use 3 digits for each number?

What about: 0 1 2 3 4 5 6 7 8 9

and

10...99

The reason it works out is because we don't use zero later

so you could think of 1 as 001 and 10 as 010

However, if the question changed to how many 7's from 100 to 1000.

Then you have 900 numbers with 3 digits = 3*900 = 2700 total digits

2700 / 10 = 270

when we actually have 280 7's from 100 to 1000. right?

I came up with the same answer for the posted question 300, by counting the 7's in different groups

1 to 9= Only one 7 (7) 10 to 99= 19 (17,27,37,47,57,67,87,97 and 70, 71, 72, 73, 74, 75, 76, 78, 79 and 77 (2 sevens)) then I knew from 100 to 1000 these 20 sevens would repeat 9 more times plus all the 7's in the hundreds digits 100 sevens from 700 to 799

1 (7) +19 (tens and ones digits from 10 to 99) +180 (tens and ones digits from 100 to 1000) +100 (hundreds digits) =300

This approach worked because when we write the numbers from 0 to 999 in the form XXX each digit take the values from 0 to 9 which provides that in the end all digits are used equal # of times.

For the range 100 to 999 it won't be so. We can solve for this range in the following way: XX7 - 7 in the units place - first digit can take 9 values (from 1 to 9) and second digit can take 10 values (from 0 to 9) --> total numbers with 7 in the units place: 9*10=90;

X7X - 7 in the tens place - first digit can take 9 values (from 1 to 9) and third digit can take 10 values (from 0 to 9) --> total numbers with 7 in the tens place: 9*10=90;

7XX - 7 in the hundreds place - second digit can take 10 values (from 0 to 9) and third digit can take 10 values (from 0 to 9) --> total numbers with 7 in the hundreds place: 10*10=100.

Re: Digits Problem Difficulty in GMAT Club test 1 [#permalink]
14 Jan 2012, 21:44

Each hundred can have 1 such number with unit digit as 1 and Tenth digit as 2, like 21, 121, 321 so we need to find number of hundred between 2 numbers, Answer 1339.

Re: Digits Problem Difficulty in GMAT Club test 1 [#permalink]
10 Aug 2013, 18:17

Bunuel wrote:

TallJTinChina wrote:

When we write the numbers 1 to 1000 do we use 3 digits for each number?

What about: 0 1 2 3 4 5 6 7 8 9

and

10...99

The reason it works out is because we don't use zero later

so you could think of 1 as 001 and 10 as 010

However, if the question changed to how many 7's from 100 to 1000.

Then you have 900 numbers with 3 digits = 3*900 = 2700 total digits

2700 / 10 = 270

when we actually have 280 7's from 100 to 1000. right?

I came up with the same answer for the posted question 300, by counting the 7's in different groups

1 to 9= Only one 7 (7) 10 to 99= 19 (17,27,37,47,57,67,87,97 and 70, 71, 72, 73, 74, 75, 76, 78, 79 and 77 (2 sevens)) then I knew from 100 to 1000 these 20 sevens would repeat 9 more times plus all the 7's in the hundreds digits 100 sevens from 700 to 799

1 (7) +19 (tens and ones digits from 10 to 99) +180 (tens and ones digits from 100 to 1000) +100 (hundreds digits) =300

This approach worked because when we write the numbers from 0 to 999 in the form XXX each digit take the values from 0 to 9 which provides that in the end all digits are used equal # of times.

For the range 100 to 999 it won't be so. We can solve for this range in the following way: XX7 - 7 in the units place - first digit can take 9 values (from 1 to 9) and second digit can take 10 values (from 0 to 9) --> total numbers with 7 in the units place: 9*10=90;

X7X - 7 in the tens place - first digit can take 9 values (from 1 to 9) and third digit can take 10 values (from 0 to 9) --> total numbers with 7 in the tens place: 9*10=90;

7XX - 7 in the hundreds place - second digit can take 10 values (from 0 to 9) and third digit can take 10 values (from 0 to 9) --> total numbers with 7 in the hundreds place: 10*10=100.

TOTAL: 90+90+100=280.

Hope it helps.

Are the numbers are not getting repeated in the above three ranges? For example , the no 777 will be part of all the three ranges above and is being counted thrice.

Re: Digits Problem Difficulty in GMAT Club test 1 [#permalink]
11 Aug 2013, 14:10

Bunuel wrote:

tonebeeze wrote:

What is the best approach to solve problems such as these two examples below. If someone can solve them and show me the steps they took, I would appreciate it greatly. The GMAT Club test explanations were a little difficult for me to digest.

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

"How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?"

Answer: 1339

Thanks Club!

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

Many approaches are possible. For example:

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) 3000/10=300 times.

Answer: 300.

2. How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?

There is one number in hundred with 2 in th tens digit and 1 in the units digit: 21, 121, 221, 321, ...

The difference between 324,700 and 458,600 is 458,600-324,700=133,900 - one number per each hundred gives 133,900/100=1,339 numbers.

i just have one question and its about this line "Now, why should ANY digit have preferences over another?" . Do you think from 1 to 1000, 1 and 0 haven't a little priority over others in aspects of their number ? i am telling because of especially the last number that is 1000 . it's not a 3 digit number but still here....... 7 was not here that's why couldn't make problem.....

By the way, one thing to tell and it's day by day i am learning lot from your uploaded files...............thanks to you again bunnel..... _________________

Re: How many times will the digit 7 be written when listing the [#permalink]
15 Aug 2014, 15:50

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Hey everyone, today’s post focuses on the interview process. As I get ready for interviews at Kellogg and Tuck (and TheEngineerMBA ramps up for his HBS... ...