How many number 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) 512
(a) 271
(b) 300
(c) 252
(d) 304
(e) 512
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Number of 7s
Source: Beat The GMAT — Problem Solving |
hi,
From :1-100 = 20 ( 7,17,27,37,47,57,67,70-79,87,97 =20 , PS=77 has two 7 digits)
From :101-200 = 20
From :201-300 = 20
From :301-400 = 20
From :401-500 = 20
From :501-600 = 20
From :601-699 = 20
From :700-800 = 20 + 100
From :801-900 = 20
From :901-1000 = 20
Total = 20x10 + 100= 300
Br,
ajp
From :1-100 = 20 ( 7,17,27,37,47,57,67,70-79,87,97 =20 , PS=77 has two 7 digits)
From :101-200 = 20
From :201-300 = 20
From :301-400 = 20
From :401-500 = 20
From :501-600 = 20
From :601-699 = 20
From :700-800 = 20 + 100
From :801-900 = 20
From :901-1000 = 20
Total = 20x10 + 100= 300
Br,
ajp
GMAT/MBA Expert
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Anurag@Gurome
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Effectively we have to find out the number of times the digit '7' appears when listing all the integers from 000 to 999. Hence, we have three places to be filled by any digit. Consider the following cases,MBA.Aspirant wrote:How many number of times will the digit '7' be written when listing the integers from 1 to 1000?
- 1. --7 : First two places can be filled by any of the 10 digits (0 to 9)
2. -7- : First and last places can be filled by any of the 10 digits (0 to 9)
1. 7-- : Last two places can be filled by any of the 10 digits (0 to 9)
The correct answer is B.
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GMAT Expert, Admissions and Career Guidance
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GMATGuruNY
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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.MBA.Aspirant wrote:How many number 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) 512
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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Student Review #3
