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digit 7

by gmatrix » Tue Aug 17, 2010 9:00 pm
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]
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by 4GMAT_Mumbai » Tue Aug 17, 2010 9:20 pm
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.
Naveenan Ramachandran
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by Rahul@gurome » Tue Aug 17, 2010 9:28 pm
gmatrix wrote: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
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by kvcpk » Tue Aug 17, 2010 9:35 pm
gmatrix wrote: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!!
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