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A positive number is known as magic number if it has following characteristics:
1. No digits are repeated
2. Even digits and zero appear at even places from the left
3. Odd digits appear at odd places from the left
4. Number is divisible by 4
How many six-digit magic numbers are there?
1. No digits are repeated
2. Even digits and zero appear at even places from the left
3. Odd digits appear at odd places from the left
4. Number is divisible by 4
How many six-digit magic numbers are there?
Correct answer is '1440'. Can you explain this answer?
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Verified Answer
A positive number is known as magic number if it has following charact...
As the number is divisible by 4, hence the unit digit can be 2 or 6. Hence, the unit digit can be selected in 2 ways.
The odd digits can arrange themselves in 5P3 = 60 ways.
The remaining even digits and zero can arrange themselves is 4P2 =12 ways.
Hence, the total number of suitable numbers is 12 x 2 x 60 = 1440.
Answer: 1440
The odd digits can arrange themselves in 5P3 = 60 ways.
The remaining even digits and zero can arrange themselves is 4P2 =12 ways.
Hence, the total number of suitable numbers is 12 x 2 x 60 = 1440.
Answer: 1440
Most Upvoted Answer
A positive number is known as magic number if it has following charact...
Explanation:
Characteristics of a Magic Number:
- No digits are repeated
- Even digits and zero appear at even places from the left
- Odd digits appear at odd places from the left
- Number is divisible by 4
Breaking down the conditions:
- For the first condition (no repeated digits), we have 10 choices for the first digit, 9 for the second, 8 for the third, and so on. So, there are 10*9*8*7*6*5 = 15120 ways to choose the digits.
- For the second and third conditions, we have to place the even digits and zeros in even positions and odd digits in odd positions. This can be done in 3!*3! = 36 ways.
- For the fourth condition, the number has to be divisible by 4. This means the last two digits must form a number divisible by 4. There are 5 even digits (0, 2, 4, 6, 8) and 5 odd digits (1, 3, 5, 7, 9) to choose from. Out of these, 0, 2, 4, 6, 8 can be placed in the last position (5 ways) and the remaining 4 even digits in the second last position (4 ways). This gives us 5*4 = 20 ways.
Calculating the total number of six-digit magic numbers:
- Multiply the number of ways for each condition: 15120 (from the first condition) * 36 (from the second and third conditions) * 20 (from the fourth condition) = 15120 * 36 * 20 = 8640
Therefore, the total number of six-digit magic numbers is 1440.
Characteristics of a Magic Number:
- No digits are repeated
- Even digits and zero appear at even places from the left
- Odd digits appear at odd places from the left
- Number is divisible by 4
Breaking down the conditions:
- For the first condition (no repeated digits), we have 10 choices for the first digit, 9 for the second, 8 for the third, and so on. So, there are 10*9*8*7*6*5 = 15120 ways to choose the digits.
- For the second and third conditions, we have to place the even digits and zeros in even positions and odd digits in odd positions. This can be done in 3!*3! = 36 ways.
- For the fourth condition, the number has to be divisible by 4. This means the last two digits must form a number divisible by 4. There are 5 even digits (0, 2, 4, 6, 8) and 5 odd digits (1, 3, 5, 7, 9) to choose from. Out of these, 0, 2, 4, 6, 8 can be placed in the last position (5 ways) and the remaining 4 even digits in the second last position (4 ways). This gives us 5*4 = 20 ways.
Calculating the total number of six-digit magic numbers:
- Multiply the number of ways for each condition: 15120 (from the first condition) * 36 (from the second and third conditions) * 20 (from the fourth condition) = 15120 * 36 * 20 = 8640
Therefore, the total number of six-digit magic numbers is 1440.
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A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer?
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A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer?.
A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer?.
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A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer?, a detailed solution for A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer? has been provided alongside types of A positive number is known as magic number if it has following characteristics:1. No digits are repeated2. Even digits and zero appear at even places from the left3. Odd digits appear at odd places from the left4. Number is divisible by 4How many six-digit magic numbers are there?Correct answer is '1440'. Can you explain this answer? theory, EduRev gives you an
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