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# How many keystrokes are needed to type numbers from 1 to 1000?

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Math Expert
Joined: 02 Sep 2009
Posts: 59712
How many keystrokes are needed to type numbers from 1 to 1000?  [#permalink]

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14 Mar 2016, 07:42
10
00:00

Difficulty:

85% (hard)

Question Stats:

50% (01:47) correct 50% (01:46) wrong based on 223 sessions

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How many keystrokes are needed to type numbers from 1 to 1000?

A. 2704
B. 2890
C. 2893
D. 3001
E. None of these

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Joined: 12 Sep 2015
Posts: 4144
Re: How many keystrokes are needed to type numbers from 1 to 1000?  [#permalink]

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14 Mar 2016, 07:52
2
1
Bunuel wrote:
How many keystrokes are needed to type numbers from 1 to 1000?

A. 2704
B. 2890
C. 2893
D. 3001
E. None of these

1-9
9 digits

10-99
There are 90 2-digit numbers
(90)(2) = 180 digits

100-999
There are 900 3-digit numbers
(900)(3) = 2700 digits

1000
4 digits

9 + 180 + 2700 + 4 = 2893
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Re: How many keystrokes are needed to type numbers from 1 to 1000?  [#permalink]

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26 Oct 2017, 15:25
2
Bunuel wrote:
How many keystrokes are needed to type numbers from 1 to 1000?

A. 2704
B. 2890
C. 2893
D. 3001
E. None of these

Each single-digit number requires 1 keystroke, so for all 9 single-digit numbers, it takes 9 total keystrokes. There are 90 double-digit numbers, each requiring 2 keystrokes, so it takes 2(90) = 180 keystrokes. For the 900 three-digit numbers, it takes 3(900) = 2,700 keystrokes, and finally, we need 4 keystrokes for 1,000. So, the total is:

9 + 180 + 2700 + 4 = 2,893

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Re: How many keystrokes are needed to type numbers from 1 to 1000?  [#permalink]

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26 Oct 2017, 22:11
it should be 9+90*2+900*3+1*4
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Re: How many keystrokes are needed to type numbers from 1 to 1000?  [#permalink]

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04 Jan 2018, 01:04
I accidentally count 0, so I picked E.
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Re: How many keystrokes are needed to type numbers from 1 to 1000?  [#permalink]

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28 Jan 2019, 09:14
1
While typing numbers from 1 to 1000, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.

There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.

There are 900 three-digit numbers: from 100 to 999.
Each of these numbers requires 3 keystrokes.
Therefore, 2700 keystrokes to type the 3-digit numbers.

1000 is a four-digit number which requires 4 keystrokes.

Totally, therefore, one requires 9 + 180 + 2700 + 4 = 2893 keystrokes.

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Re: How many keystrokes are needed to type numbers from 1 to 1000?  [#permalink]

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05 Feb 2019, 04:07
Bunuel wrote:
How many keystrokes are needed to type numbers from 1 to 1000?

A. 2704
B. 2890
C. 2893
D. 3001
E. None of these

1 to 9 : 9 digits
10to99= 90*2 = 180 digits
100 to 999 = 900 * 3 = 2700 digits
1000 = 4 digits
9+180+2700+4
2893
IMO C
Re: How many keystrokes are needed to type numbers from 1 to 1000?   [#permalink] 05 Feb 2019, 04:07
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