GMAT Math Questions - Number Systems
March 16, 2004
How many keystrokes are needed to type numbers from 1 to 1000?
| (A) | 3001 |
| (B) | 2893 |
| (C) | 2704 |
| (D) | 2890 |
| (E) | None of these |
Correct Choice (B) - Correct Answer (2893)
Solution:
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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