Last visit was: 17 May 2024, 21:15 It is currently 17 May 2024, 21:15
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In writing all of the integers from 1 to 300, how many times is the di

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624556 [12]
Given Kudos: 81898
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 8023
Own Kudos [?]: 4122 [1]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11264
Own Kudos [?]: 32571 [2]
Given Kudos: 306
Intern
Joined: 10 Sep 2018
Posts: 41
Own Kudos [?]: 54 [3]
Given Kudos: 72
Re: In writing all of the integers from 1 to 300, how many times is the di [#permalink]
1
Kudos
1
Bookmarks
Lets go range wise 1- 100

Digit one can appear at any of the following places

Units , Tens and hundreds

Units
in a range of 1-100
1,11,21,31......91 i.e 10 times in a 100
so total occurence in 300 will be 3 *10 = 30

tens
10,11,12,13......19 =10times in a hundres
again total occurences in 300 will be 3 * 10= 30

hundreds
100 , 101, 102 ....109,....199 = 100 places

total = 30 +30 +100= 160
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18873
Own Kudos [?]: 22258 [0]
Given Kudos: 285
Location: United States (CA)
Re: In writing all of the integers from 1 to 300, how many times is the di [#permalink]
Bunuel wrote:
In writing all of the integers from 1 to 300, how many times is the digit 1 used?

A. 30
B. 60
C. 130
D. 160
E. 161

From 10 to 19, the digit 1 is used 11 times. For all other numbers from 1 to 99, it’s used a total of 9 times. So, it’s used a total of 20 times.

From 110 to 119, the digit 1 is used 21 times. For all other numbers from 100 to 199 it’s used 90 + 9 = 99 times. So, it’s used a total of 120 times.

From 210 to 219 the digit 1 is used 11 times. For all other numbers, from 200 to 300, it’s used 9 times, so it’s used a total of 20 times.

In total, the digit 1 is used 160 times.

GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30243 [1]
Given Kudos: 799
Re: In writing all of the integers from 1 to 300, how many times is the di [#permalink]
1
Bookmarks
Top Contributor
Bunuel wrote:
In writing all of the integers from 1 to 300, how many times is the digit 1 used?

A. 30
B. 60
C. 130
D. 160
E. 161

Let's consider the values from 000 to 299
NOTE: Yes, I have started at 000 and ended at 299, even though though the question asks us to look at the numbers from 1 to 300.
HOWEVER, notice that 000 and 299 do not have any 1's so the outcome will be the same.

Okay, there are 300 integers from 000 to 299

UNITS position
Each of the 10 digits (0, 1, 2, 3..., 9) appears the same number of times in the UNITS position.
So, the digit 1 must occur 1/10 of the time in this position.
So, the digit 1 must appear (1/10)(300) times, which equals 30 times.

TENS position
Each of the 10 digits (0, 1, 2, 3..., 9) appears the same number of times in the TENS position.
So, the digit 1 must occur 1/10 of the time in this position.
So, the digit 1 must appear (1/10)(300) times, which equals 30 times.

HUNDREDS position
The 1 appears in the HUNDREDS position in every integer from 100 to 199
So, the digit 1 appears 100 times.

TOTAL = 30 + 30 + 100
= 160

Cheers,
Brent
Intern
Joined: 08 Mar 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Re: In writing all of the integers from 1 to 300, how many times is the di [#permalink]
There is no need to count! Here is a simple approach:

_ _ 1 : we have one fixed in the units, on the hundreds we have 1 to 3 to choose, that's 3c1, which is 3, and in the tens we have 0 to 9 to choose, 1 out of 10 digits, that's 10c1, which is 10. Hence, 3*10*1= 30

Move the 1 to the left:
_ 1 _ : we have one fixed in the tens, on the hundreds we have 1 to 3 to choose, that's 3c1, which is 3, and in the units we have 0 to 9 to choose, 1 out of 10 digits, that's 10c1, which is 10. Hence, 3*1*10= 30

Move the 1 to the left again:
1 _ _ : we have one fixed in the hundreds, in the units we have 0 to 9 to choose, 1 out of 10 digits, that's 10c1, which is 10. and in the tens we have 0 to 9 to choose, 1 out of 10 digits, that's 10c1, which is 10. Hence, 1*10*10= 100

Adding all up we get 160
Non-Human User
Joined: 09 Sep 2013
Posts: 33058
Own Kudos [?]: 828 [0]
Given Kudos: 0
Re: In writing all of the integers from 1 to 300, how many times is the di [#permalink]
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.
Re: In writing all of the integers from 1 to 300, how many times is the di [#permalink]
Moderators:
Math Expert
93334 posts
Senior Moderator - Masters Forum
3137 posts