A typewriter can type digits at a speed of 5 digits per sec.

Odd numbers which have only one digit: 1, 3, ..., 9 - a total of (9 - 1)/2 + 1 = 5 numbers
Odd numbers which have exactly two digits - 11, 13, ..., 99 - altogether (99 - 11)/2 + 1 = 45 numbers
Finally, odd numbers with exactly three digits - 101, 103, ..., 999 - a total of (999 - 101)/2 + 1 = 450 numbers.

The total number of digits is 5*1 + 45*2 + 450*3.
The time needed to type them (in seconds) is (5 + 45*2 + 450*3)/5 = 1 + 18 + 270 = 289.

Answer C.
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Hi All,

The 'math' behind this question can be done in a couple of different ways; it's really a matter of 'when' you want to take 'half' of the possibilities.

Since the question requires that we figure the number of digits in all of the ODD integers up to 1,000.....we can figure out the total number of digits, then remove half of them (since half of the numbers up to 1000 are odd):

10 1-digit numbers = 10 digits
90 2-digit numbers = 180 digits
900 3-digit numbers = 2700 digits

10 + 180 + 2700 = 2890 digits

By dividing by 2, we remove all of the ODD numbers from the group.

2890/2 = 1445 digits

Since the typewriter can type 5 digits per second, we have....

1445/5 = 289 seconds.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Asked: A typewriter can type digits at a speed of 5 digits per second. If it is used to type all the odd natural numbers till 1000 then how much time(in seconds) will be needed?

Odd natural numbers = {1,3,5,7,9, 11-99, 101-999}
1 digit odd natural numbers = 5 digits to be typed in 1 second
2 digit odd natural numbers = 2*((99-11)/2 +1) = 45*2 = 90 digits to be typed in 18 seconds
3 digit odd natural numbers = 3*((999-101)/2+1) = 450*3 = 1350 digits to be typed in 270 seconds

Total time needs in seconds = 1 + 18 + 270 = 289 seconds

IMO C

total 1 digit odd no ; ( 9-1)/2+1 ; 5
total 2 digit odd no ; ( 99-11)/2+1 ;45
total 3 digit odd no ; ( 999-101)/2+1 ; 450
total ; 450*3+45*2+5*1 ; 1445/5 ; 289
IMO C

Might be a stupid question but can someone explain how to come up with this equation:

Odd numbers which have only one digit: 1, 3, ..., 9 - a total of (9 - 1)/2 + 1 = 5 numbers
Odd numbers which have exactly two digits - 11, 13, ..., 99 - altogether (99 - 11)/2 + 1 = 45 numbers
Finally, odd numbers with exactly three digits - 101, 103, ..., 999 - a total of (999 - 101)/2 + 1 = 450 numbers.

I got it right eventually but I counted a bit through in my mind.
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