digit 7

[gmatrix]

Source:gmat club tests

How many times will the digit 7 be written when listing the integers from 1 to 1000?
[spoiler]OA: 300 [/spoiler]

[4GMAT_Mumbai]

Hi,

Let us take tranches of numbers to understand this

1 - 69 -> 7
70-79 -> 11
80 - 100 -> 2

Hence, for every hundred numbers, there are 20 (7+11+2) sevens to be written.

For each of the 10 tranches of 100 numbers in the group 1 to 1000, we have 20 sevens to be written.

Hence, there are 200 sevens.

For the tranche 700 - 799, there are 100 more sevens arising from the hundredth position.

Hence, a total of 300 sevens.

Hope this helps. Thanks.

[Rahul@gurome]

Source:gmat club tests

How many times will the digit 7 be written when listing the integers from 1 to 1000?
[spoiler]OA: 300 [/spoiler]

When 7 is at units place, tens and hundreds place can be filled with digits 0 to 9.
10*10*1 = 100
Similarly, when 7 is at tens place, units and hundreds place can be filled in 100 ways again. (10*1*10 = 100)
When 7 is at hundreds place, units and tens place can be filled in 10*10 = 100 ways.

100 + 100 + 100 = 300 ways in total

[kvcpk]

Source:gmat club tests

How many times will the digit 7 be written when listing the integers from 1 to 1000?
[spoiler]OA: 300 [/spoiler]

X or XX or XXX
for X -> 1 way
for XX -> X7 or 7X -> 19 ways
for XXX ->
7XX -> 100 ways
X7X -> 90 ways
XX7 -> 90 ways

total = 1+19+100+90+90 = 300

Hope this helps!!