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?
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.
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.
1. Number Systems | Types of Numbers | Chart
2. Number Properties | Rational & Irrational Numbers
3. GMAT Number Properties | Indices & Rule of Exponents
4. Number Systems | Surds & Conjugates
5. Number Properties | Tests of divisibility
6. Number Properties | How to check whether a number is prime?
7. Number Properties | How to prime factorize a number?
8. GMAT Number Theory | Prime factorization | Properties of squares & cubes
9. Number Properties | What is HCF? | How to find HCF?
10. Number Properties | What is LCM? | How to find LCM?
11. 3 important properties of LCM & HCF | LCM & HCF of fractions
12. Number Properties | When to use LCM and HCF?
13. Number Theory | How to find number of factors?
14. Number Theory | Number of ways to express as a product of 2 factors
15. Number Theory | Sum of all factors of a number
16. Number Theory | Product of all factors of a number
17. Number Theory | Remainders of sum & product
18. Number Theory | Remainder of dividing xn by 'd'
19. Polynomials | Remainder when a monomial divides it
20. Number Theory | Highest power of a prime that divides factorial of 'n'
21. Number Theory | Highest power of a composite number that divides factorial of 'n'
22. Number Theory | Number of trailing zeroes in a number
23. Number Theory | Unit digit of higher powers of numbers
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