GMAT Maths | GMAT Number Properties

GMAT Sample Questions | Number Systems & Counting Methods

This GMAT problem solving question tests concepts in counting methods and elementary number properties. A GMAT 600 level sample question, solving which requires knowing very basic properties of number of single digit, two-digit and three-digit numbers.

Question 4: How many keystrokes are needed to type numbers from 1 to 1000?

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

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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.

Watch out for the common mistake that many of us make of counting only 89 2-digit numbers and 899 3-digit numbers. The temptation is to say, 99 - 10 = 89. So, 89 2-digit numbers exist. 99 - 10 means that we are not counting 10 as a 2-digit number. The correct approach is: of the 99 numbers from 1 to 99, we are not counting the first 9 single digit numbers. So, we have 99 - 9 = 90 2-digit numbers. The same logic applies when we count 3-digit numbers.


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