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The question is a counting Methods problem. Number Theory and Number Properties are hot favorites in GMAT.

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

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

The correct choice is (B) and the correct answer is 2893.

While typing numbers from 1 to 1000, you have 9 single digit numbers from 1 to 9. Each of them require one keystroke. That is 9 key strokes.

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

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

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

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

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