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How many times is the digit "3" written while numbering the pages of a book from 1 to 1000?

let me give it a try :
from 1-100 the no. of 3's is 20
similiarily from 101-200 no. of 3's is 20
similiarily from 201-299 no. of 3's is 20
similiarily from 401-500 no. of 3's is 20
similiarily from 501-600 no. of 3's is 20
similiarily from 601-700 no. of 3's is 20
similiarily from 701-800 no. of 3's is 20
similiarily from 801-900 no. of 3's is 20
similiarily from 901-100 no. of 3's is 20

No. of 3's between 300-400 no.s of 3's are 20+100

Hence total no. of 3's are 180+100 = 280

Kindly advise if i have done something wrong in this .

Actually the count will be 300. 10*20 + 100=300
there will be 120 3's between 300-400.

The answer is 300.

Mad - '3' is written 120 times between 300 and 399 as pointed out by you. So, the total should be 180 + 120 = 300.

yeah.. that's correct .... i am sorry i missed it !

Thank you for the answers on no of 3's. Are there any new material for GMAT?

Thank you for the help

Here is an alternate approach.

As 1000 does not have a '3' in it, we can restrict our count up to 999.

Look at any number up to 999 as a 3 digit number. Makes life easy that way.

So, we will imagine writing a 34 as 034 and an 8 as 008.

So, the number of cases where '3' happens to be the unit digit upto 999 = 10 * 10 * 1.
The login being that, the Hundreds place can take any digit from 0 to 9 (10 options), the tens place can take any digit from 0 to 9 (10 options). Therefore, there will be 100 numbers from 1 to 999 in which '3' will be the unit digit.

The same logic holds for '3' being in the 10s place and in the 100s place.

So, the total number of 3s written will be sum of all these 3 cases = 300.