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Count of numbers

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Count of numbers

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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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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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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