Count of numbers

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confuse mind: Master | Next Rank: 500 Posts; Posts: 462; Joined: Wed Jan 19, 2011 1:08 pmFollowed by: 4 members; Thanked: 10 times

by confuse mind » Sat Jul 21, 2012 7:29 pm

How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?
A. 6
B. 7
C. 5
D. 8
E. 18

[spoiler]
IMO - B
1 000 000

sol:
1 in place of each of 6 zeroes - 6
2 000 000 - 1

thus total = 7[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sat Jul 21, 2012 7:29 pm

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Jul 21, 2012 8:32 pm

confuse mind wrote:How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?
A. 6
B. 7
C. 5
D. 8
E. 18

[spoiler]
IMO - B
1 000 000

sol:
1 in place of each of 6 zeroes - 6
2 000 000 - 1

thus total = 7[/spoiler]

Assuming you meant 10^6 and 10^7 - correct.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jul 21, 2012 8:44 pm

confuse mind wrote:How many different positive integers exist between 10^6 and 10^7, the sum of whose digits is equal to 2?

10^6 = 1,000,000

As 2 = 1 + 1 = 2 + 0
We can have 6 integers starting with 1 with sum of digits equal to 2 and one integer starting with 2.

Hence, a total of (6 + 1) = 7 integers.

The correct answer is B.

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