It is currently 14 Dec 2017, 00:21

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# the principle of coounting?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Feb 2010
Posts: 205

Kudos [?]: 46 [0], given: 1

### Show Tags

04 Jul 2011, 09:01
hi all,
is there a quicker way to solve this problem? Thanks!

How many times will the digit 7 be written when listing the integers from 1 to 1000?

(C) 2008 GMAT Club - m01#10

110
111
271
300
304
There are several ways to count the number of times 7 appears between 7 and 997. One way is to consider the number of 7's in single, double, and triple digit numbers separately.

One-digit numbers: 7 is the only one-digit number.

Two-digit numbers: 7 could be the first digit or the second digit. Case 1: 7 is the first digit. There are 9 ways to place 7 as the first digit of a two-digit number. Case 2: There are 10 ways to place the second digit, i.e. 0-9. Remember that we have counted 07 already. Thus, for two-digit numbers we have: numbers that contain a 7.

Three-digit numbers: Use the knowledge from the previous two scenarios: each hundred numbers will contain one 7 in numbers such as 107 or 507 and also 19 other sevens in numbers such as 271 or 237. Thus a total of 20 sevens per each hundred and 200 sevens for 1000. Since we have 700's within the range, that adds another 100 times that a seven will be written for a total of 300 times.

Kudos [?]: 46 [0], given: 1

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7793

Kudos [?]: 18124 [0], given: 236

Location: Pune, India
Re: the principle of coounting? [#permalink]

### Show Tags

05 Jul 2011, 02:36
Another approach:
7 in unit's place:
In every 10 consecutive numbers, 7 will appear once. Since we have 1000 numbers, we have 100 sequences of 10 consecutive numbers (1-10, 11-20 etc) so 7 will appear in unit's place 100 times.
7 in ten's place:
In every 100 consecutive numbers, 7 appears in ten's place 10 times (from 70 to 79). We have 10 sequences of 100 consecutive numbers (1-100, 101-200 etc) so we get that 7 will appear in ten's place 10*10 = 100 times.
In every 1000 numbers, 7 will appear in hundred's place 100 times (from 700 to 799).
Total = 100 + 100 + 100 = 300
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18124 [0], given: 236

Manager
Joined: 20 Dec 2010
Posts: 240

Kudos [?]: 53 [0], given: 4

Schools: UNC Duke Kellogg
Re: the principle of coounting? [#permalink]

### Show Tags

06 Jul 2011, 05:14
Very clever solution from the Veritas instructor!

Kudos [?]: 53 [0], given: 4

Re: the principle of coounting?   [#permalink] 06 Jul 2011, 05:14
Display posts from previous: Sort by