digit 7

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gmatrix: Master | Next Rank: 500 Posts; Posts: 108; Joined: Fri Jul 09, 2010 8:15 am; Location: 127.0.0.1; Thanked: 15 times

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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Source: Beat The GMAT — Problem Solving | Tue Aug 17, 2010 9:00 pm

4GMAT_Mumbai: Master | Next Rank: 500 Posts; Posts: 161; Joined: Mon Apr 05, 2010 9:06 am; Location: Mumbai; Thanked: 37 times

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
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

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

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

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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don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
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