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Manager  Joined: 29 Nov 2011
Posts: 71
A typewriter can type digits at a speed of 5 digits per sec.  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 51% (02:13) correct 49% (01:49) wrong based on 134 sessions

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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?

(a) 199
(b) 200
(c) 289
(d) 578
(d) None of these
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: A typewriter can type digits at a speed of 5 digits per sec.  [#permalink]

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Smita04 wrote:
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?

(a) 199
(b) 200
(c) 289
(d) 578
(d) None of these

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.

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A typewriter can type digits at a speed of 5 digits per sec.  [#permalink]

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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.

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Re: A typewriter can type digits at a speed of 5 digits per sec.  [#permalink]

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Smita04 wrote:
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?

(a) 199
(b) 200
(c) 289
(d) 578
(d) None of these

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
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Re: A typewriter can type digits at a speed of 5 digits per sec.  [#permalink]

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Smita04 wrote:
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?

(a) 199
(b) 200
(c) 289
(d) 578
(d) None of these

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
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Re: A typewriter can type digits at a speed of 5 digits per sec.  [#permalink]

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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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Go kick in the door. Re: A typewriter can type digits at a speed of 5 digits per sec.   [#permalink] 02 Sep 2019, 23:00
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