Latest self Aptitude Question SOLUTION: Given that 2^2004 is a 604-digit number whose first digit is 1, how many elements of the set S = {2^0,2^1,2^3...,2^2003} have a first digit of 4?

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(#M40010214) SELF Numerical Ability question Keep an EYE

Given that 2^2004 is a 604-digit number whose first digit is 1, how many elements of the set S = {2^0,2^1,2^3...,2^2003} have a first digit of 4?

chaitanya (11 years ago)

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Aman  (11 years ago)

195 elements of the set S = {2^0,2^1,2^3...,2^2003} have a first digit of 4.

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prashanthi  (11 years ago)

has digits and starts with a , there are numbers of digits for the powers of from to .


so

where is the number of numbers of digits that have powers of , and is the number of numbers of digits that have powers of . We're looking for .

Solving for , the answer is 195

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Lekshmana Perumal  (7 years ago)

this problem is from book 104 Number Theory Problems: From the Training of the USA IMO Team

i explained answer in details in below

The smallest power of 2 with a given number of digits has a first digit of 1, and there are elements of S with n digits for each integer n

Is this solution Helpfull? Yes | No   

Lekshmana Perumal  (7 years ago)

this problem is from book 104 Number Theory Problems: From the Training of the USA IMO Team

i explained answer in details in below

The smallest power of 2 with a given number of digits has a first digit of 1, and there are elements of S with n digits for each integer n

Is this solution Helpfull? Yes | No   

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