integers

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Sep 01, 2018 6:13 am

vaibhav101 wrote:how many numbers of times will the digit 7 be written when listing the integers from 1 to 1000?

A 271
B 300
C 252
D 304
E 204

Here's one way to look at it.
Write all of the numbers as 3-digit numbers.
That is, 000, 001, 002, 003, .... 998, 999

NOTE: Yes, I have started at 000 and ended at 999, even though though the question asks us to look at the numbers from 1 to 1000. HOWEVER, notice that 000 and 1000 do not have any 7's so the outcome will be the same.

First, there are 1000 integers from 000 to 999
There are 3 digits in each integer.
So, there is a TOTAL of 3000 individual digit. (since 1000 x 3 = 3000)

Each of the 10 digits is equally represented, so the 7 will account for 1/10 of all digits.

1/10 of 3000 = 300

So, there are 300 0's, 300 1's, 300 2's, 300 3's, . . ., and 300 9's in the integers from 000 to 999

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Sep 01, 2018 6:25 am

vaibhav101 wrote:how many numbers of times will the digit 7 be written when listing the integers from 1 to 1000?

A 271
B 300
C 252
D 304
E 204

If we use 0 as a placeholder -- so that 007 represents 7, 072 represents 72, etc. -- then we need to count the number of times that 7 will appear among the 3-digit integers from 000 to 999, inclusive.

Total number of 3-digit integers from 000 to 999, inclusive = biggest - smallest + 1 = 999-000+1 = 1000.

Each of these 1000 integers includes 3 digits.
Thus, the total number of digit appearances = 3*1000 = 3000.

Among these 3000 digit appearances, each of the 10 digits will appear the same number of times.
Thus, the number of times that 7 will appear = 3000/10 = 300.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Sep 11, 2018 4:19 pm

vaibhav101 wrote:how many numbers of times will the digit 7 be written when listing the integers from 1 to 1000?

A 271
B 300
C 252
D 304
E 204

The digit 7 as the hundreds digit appears 100 times (700 to 799). As the tens digit, it appears 100 times also (ten times each in the 70s, 170s, 270s, ..., 970s). As the units digit, it appears 100 times also (7, 17, 27, ..., 997). Therefore, the digit 7 has appeared a total of 300 times.

Answer: B

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