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Sum of the Digits is 2

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by ArunangsuSahu » Fri Nov 11, 2011 8:50 pm
Find out how many numbers between 10^6 and 10^7 have the sum of their digits as 2?

(A) 6
(B) 7
(C) 14
(D) 5
(E) None Of These
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by Anurag@Gurome » Fri Nov 11, 2011 8:57 pm
ArunangsuSahu wrote:Find out how many numbers between 10^6 and 10^7 have the sum of their digits as 2?
Sum of digits of a number can be 2 only if either it is made of only one 2 and rest zeroes or two 1s and rest zeroes.

Number of such numbers between 1,000,000 and 10,000,000, i.e. such a seven digit number,
  • 1. Two 1s and rest zeroes ---> Seven digit number starting with 1 and the other 1 can be in any other 6 places. Hence 6 such numbers.
    2. One 2 and rest zeroes ---> Seven digit number starting with 2. Only one such number is possible.
Hence, total number of such integers in the given range = (6 + 1) = 7

The correct answer is B.
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by ArunangsuSahu » Sat Nov 12, 2011 5:36 am
Right..
6P1+1=7
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by vaibhavgupta » Sun Nov 13, 2011 9:36 pm
ArunangsuSahu wrote:Find out how many numbers between 10^6 and 10^7 have the sum of their digits as 2?

(A) 6
(B) 7
(C) 14
(D) 5
(E) None Of These
+1 for B!
If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A

FML!! :/
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