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

Question

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

NCRanjan · Accepted Answer

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

Archit3110 · Answer

chetan2u  :
Instead of counting all no.s is there any shortcut to solve such a question ;?

chetan2u · Answer

Hi,

The digit 1 can be at any of the three places -
1) hundred - 100-200 will have 100 places where 1 is used.
2) tens - Now if we take last two digits 00,01,02,03....97,98,99.. total 100 numbers
Here each of the digits 0 to 9 will be equally used so 100/10=10
3) ones ...
There are 100 digits at units place in 00,01,02,...97,98,99
Again all digits will be used equally so 100/10=10..

So digit 1 is used at..
1) hundreds - 100 places
2) tens - 10 * 3=30, as there are 3 century (01-100; 101-200; 201-300), we are looking at
3) ones - 10*3=30, same as above 
So 100+30+30=160

D

ScottTargetTestPrep · Answer

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.

Answer: D

BrentGMATPrepNow · Answer

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

Answer: D

Cheers,
Brent

Charlie2017 · Answer

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

bumpbot · Answer

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.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards