Number Properties - Counting Methods

Concept: Counting Methods, Digits, Numbers

This GMAT problem solving question tests concepts in counting methods.

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

  1. 3001
  2. 2893
  3. 2704
  4. 2890
  5. None of these

Video Explanation

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Explanatory Answer

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.

Choice B is the correct answer.

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