still integers

[demoskopico]

How many times will the digit 7 be written when listing the integers from 1 to 1000?
 110
 111
 271
 300
 304

OA is D.

What is wrong in my calculus?

For every hundred we have 7,17,27,37,47,57,67,77,87,97: 10 integers ending in 7. for every hundred but the 7th than we have 90 inetgers
For the tenth series of every hundred we have 70,71,72,73,74,75,76,78,79 (we must get rid of 7 because we considered it in the first step). For every hundred but the 7th we have 9*9=81 integers
Then we must consider the 100 numbers from 700 to 800=100

100+81+90=271. what is my mistake?

[kevin]

How many three digit numbers can be written with only one 7? Choose which digit will be a 7, and then decide on the other two digits (can be any of the 9 other digits)

3 *9*9=243

What about with two 7´s ? (choose which digit will not be a seven, and then decide what this digit will be)

3 *9= 27

What about with three 7's?

1

243 + 54 + 3 = 300

[demoskopico]

How many three digit numbers can be written with only one 7?

3 *9*9=243

What about with two 7´s ?

3 *9= 27

What about with three 7's?

1

243 + 54 + 3 = 300


How come this:

3 *9*9=243



3 *9= 27

[lakhianihersh@yahoo.com]

in my view question needs to be solved like this

first digit as 7 other two places can be filled with 9 diff nos ( this includes 0)
so number can be like 7_ _ since 9 digits can be filled therfore total numbers can be 9 * 9 that is 81

secondly, when 7 at the position 2 that is _ 7 _ = first place will take 8 as 0 cannot take the first place therefore 8 hence total will be 8*9 = 72

thirdly 7 at last position total will be 72 again

therfore answer should be 225

[demoskopico]

in my view question needs to be solved like this

first digit as 7 other two places can be filled with 9 diff nos ( this includes 0)
so number can be like 7_ _ since 9 digits can be filled therfore total numbers can be 9 * 9 that is 81

secondly, when 7 at the position 2 that is _ 7 _ = first place will take 8 as 0 cannot take the first place therefore 8 hence total will be 8*9 = 72

thirdly 7 at last position total will be 72 again

therfore answer should be 225

OA is 300

first hundred: unit:10, tenth : 10 (77 has 2 seven and this is the key:we must count it twice!)
let's multiply by 20*10=200

then, we must add up all the numbers relative to the 700 hundred: we have 100 numbers

200+100=300