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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 answer is option 'B'. Can you explain this answer?
Verified Answer
How many keystrokes are needed to type numbers from 1 to 1000?a)3001b)...
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.
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.
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.
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.
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.
Most Upvoted Answer
How many keystrokes are needed to type numbers from 1 to 1000?a)3001b)...
Introduction
To determine the total number of keystrokes needed to type all the numbers from 1 to 1000, we must calculate the total digits used in these numbers.
Counting Digits by Ranges
1. Numbers 1 to 9 (1-digit numbers)
- Total numbers: 9
- Total digits: 9 (1 digit each)
2. Numbers 10 to 99 (2-digit numbers)
- Total numbers: 90 (from 10 to 99)
- Total digits: 90 * 2 = 180 (2 digits each)
3. Numbers 100 to 999 (3-digit numbers)
- Total numbers: 900 (from 100 to 999)
- Total digits: 900 * 3 = 2700 (3 digits each)
4. Number 1000 (4-digit number)
- Total digits: 4 (only one number)
Calculating Total Keystrokes
- Total from 1 to 9: 9
- Total from 10 to 99: 180
- Total from 100 to 999: 2700
- Total from 1000: 4
Final Calculation
- Total keystrokes: 9 + 180 + 2700 + 4 = 2893
Thus, the correct answer is option 'B' with a total of 2893 keystrokes needed to type all the numbers from 1 to 1000.
To determine the total number of keystrokes needed to type all the numbers from 1 to 1000, we must calculate the total digits used in these numbers.
Counting Digits by Ranges
1. Numbers 1 to 9 (1-digit numbers)
- Total numbers: 9
- Total digits: 9 (1 digit each)
2. Numbers 10 to 99 (2-digit numbers)
- Total numbers: 90 (from 10 to 99)
- Total digits: 90 * 2 = 180 (2 digits each)
3. Numbers 100 to 999 (3-digit numbers)
- Total numbers: 900 (from 100 to 999)
- Total digits: 900 * 3 = 2700 (3 digits each)
4. Number 1000 (4-digit number)
- Total digits: 4 (only one number)
Calculating Total Keystrokes
- Total from 1 to 9: 9
- Total from 10 to 99: 180
- Total from 100 to 999: 2700
- Total from 1000: 4
Final Calculation
- Total keystrokes: 9 + 180 + 2700 + 4 = 2893
Thus, the correct answer is option 'B' with a total of 2893 keystrokes needed to type all the numbers from 1 to 1000.
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Community Answer
How many keystrokes are needed to type numbers from 1 to 1000?a)3001b)...
To determine the total number of keystrokes needed to type all the numbers from 1 to 1000, we need to calculate the total digits used in these numbers.
Let's break it down by ranges:
1. Numbers 1 to 9 (1-digit numbers):
- Total numbers: 9
- Total digits: 9 (1 digit each)
2. Numbers 10 to 99 (2-digit numbers):
- Total numbers: 90 (from 10 to 99)
- Total digits: 90 * 2 = 180 (2 digits each)
3. Numbers 100 to 999 (3-digit numbers):
- Total numbers: 900 (from 100 to 999)
- Total digits: 900 * 3 = 2700 (3 digits each)
4. Number 1000 (4-digit number):
- Total digits: 4 (only one number)
Now, let's calculate the total keystrokes:
- Total from 1 to 9: 9
- Total from 10 to 99: 180
- Total from 100 to 999: 2700
- Total from 1000: 4
Final Calculation:
Total keystrokes: 9 + 180 + 2700 + 4 = 2893
Therefore, the correct answer is indeed option 'B' with a total of 2893 keystrokes needed to type all the numbers from 1 to 1000.
Let's break it down by ranges:
1. Numbers 1 to 9 (1-digit numbers):
- Total numbers: 9
- Total digits: 9 (1 digit each)
2. Numbers 10 to 99 (2-digit numbers):
- Total numbers: 90 (from 10 to 99)
- Total digits: 90 * 2 = 180 (2 digits each)
3. Numbers 100 to 999 (3-digit numbers):
- Total numbers: 900 (from 100 to 999)
- Total digits: 900 * 3 = 2700 (3 digits each)
4. Number 1000 (4-digit number):
- Total digits: 4 (only one number)
Now, let's calculate the total keystrokes:
- Total from 1 to 9: 9
- Total from 10 to 99: 180
- Total from 100 to 999: 2700
- Total from 1000: 4
Final Calculation:
Total keystrokes: 9 + 180 + 2700 + 4 = 2893
Therefore, the correct answer is indeed option 'B' with a total of 2893 keystrokes needed to type all the numbers from 1 to 1000.
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