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Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :
I. It contains all digits from 1 to n, and all of them are used exactly once.
II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).

To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)
It is known that he uses 6 digit passwords for leisure files, which are his most important files. 
 
 
Q. How many leisure passwords are possible?
    Correct answer is '2'. Can you explain this answer?
    Verified Answer
    Darren Puppet, the richest person in the world, has ensured extra secu...
    Solution: As seen in the previous solution, four digits are fixed, we are left with a and c, which can be either 1 or 3.
    We have only 2 possible leisure passwords, 123654 and 321654.
    Answer: 2
    View all questions of this test
    Most Upvoted Answer
    Darren Puppet, the richest person in the world, has ensured extra secu...
    Understanding the 6-Digit Password Criteria
    To find the number of valid 6-digit passwords composed of the digits 1 to 6, we need to ensure they meet specific divisibility conditions.
    Divisibility Rules for Passwords
    - The number formed by the first 2 digits must be divisible by 2.
    - The number formed by the first 3 digits must be divisible by 3.
    - The number formed by the first 4 digits must be divisible by 4.
    - The number formed by the first 5 digits must be divisible by 5.
    - The number formed by all 6 digits must be divisible by 6.
    Applying the Conditions
    1. Divisibility by 2: The last digit of the first two digits must be even. Therefore, the options are 2, 4, or 6.
    2. Divisibility by 3: The sum of the first three digits must be divisible by 3. The sum of digits 1 through 6 is 21, which is divisible by 3, so any combination of three digits will satisfy this condition.
    3. Divisibility by 4: The number formed by the first four digits must end in a number that makes it divisible by 4. The last two digits of these four must form a number divisible by 4.
    4. Divisibility by 5: The fifth digit must be 5, as it is the only option from 1 to 6 that ensures the number formed by the first five digits is divisible by 5.
    5. Divisibility by 6: Since we already established that the sum of all digits is 21 (divisible by 3) and the last digit must be even, the sixth digit must be one of the even numbers.
    Valid Combinations
    After analyzing the conditions, only two combinations satisfy all rules:
    - 123564
    - 321654
    Conclusion
    Thus, the total number of valid 6-digit passwords Darren can use is 2.
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    The chief scientist of a major vaccine producing company has the responsibility to keep the formula of the vaccine confidential. He stores the formula in his e-device with 3 consecutive locks, all of which need to be unlocked to access the formula. The first of the 3 locks is a pattern lock, the second one is a numeric lock and the third and final one is an alphanumeric lock. The pattern lock is in the form of a regular hexagon with 6 distinct vertices A1, A2, A3, A4, A5, A6, in that order. One needs to connect all the 6 vertices one after the another in any random order connecting each vertex only once and only one order of connecting the 6 vertices exists which will unlock the first lock. The numeric lock has a code of ABC, where A, B and C are single digit natural numbers. A is a multiple of 2. B is a multiple of 3, C is a multiple of 4 but not equal to A.The alphanumeric lock has a code MNPQRS, where M and N are alphabets and P, Q, R and S are digits. M and N have to be consecutive vowels or consecutive consonants, not necessarily in order. Two alphabets are said to be consecutive vowels if both of them are vowels and they are consecutive when all the 5 vowels are written in alphabetical order. For example, E and I are consecutive vowels, but A and O are not. Two alphabets are said to be consecutive consonants if both of them are consonants and they are consecutive when all the 21 consonants are written in alphabetical order. For example, D and F are consecutive consonants but D and V are not. For example, M and N can be A and E respectively or E and A respectively. P is equal to Base-Ten-Index of M. Q is equal to the Base-Ten-Index of N. R and S can only take binary values, that is, 0 or 1.Base-Ten-Index of an alphabet = Index of alphabet % 10, where Index of an alphabet is its position when all alphabets from A to Z are arranged alphabetically and a%b is the remainder when a is divided by b.For example, Base-Ten-Index of J = 10 = 0 , Base-Ten-Index of M = 13 = 3.The chief scientist can only set passwords/patterns which follow all of the conditions mentioned above.Based on the information given above, answer the questions that follow.Q.Given below is a list of patterns/passwords, some of which are in accordance with the rules mentioned and some are not. The chief scientist can use any combination of valid patterns/passwords from the following to lock the e-device. What is the total number of ways in which he can do so?Pattern:(1) A1 A2 A5 A6 A5 A2 A4 (2) A1 A2 A3 A4 A5 A6 (3) A6 A5 A4 A3 A2 A1 (4) A1 A6 A5 A2 A4Numeric password:(1) 234 (2) 434 (3) 298 (4) 634 (5) 894 (6) 230 (7) 638Alphanumeric password:(1) AE1500 (2) CD3410 (3) HJ8000 (4)QP7600 (5) AB1211 (6) YZ4600 Correct answer is '40'. Can you explain this answer?

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    Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer?
    Question Description
    Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. 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 Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer?.
    Solutions for Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
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How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer?, a detailed solution for Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer? has been provided alongside types of Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Darren Puppet, the richest person in the world, has ensured extra security for his files. He implements a security based on division algorithms in his passwords. The passwords contain n digits such that :I. It contains all digits from 1 to n, and all of them are used exactly once.II. The number formed by the first two digits is divisible by 2, the number formed by the first 3 digits is divisible by 3, and so on such that the n digit password is divisible by n. (For example, 123 is such a 3 digit password, 12 is divisible by 2 and 123 by 3).To remember which password he is using, Darren ranks all the passwords having certain number of digits in increasing order and hence by just knowing the number of digits and the rank, he is able to correctly enter the password. (For example, for 3 digits passwords, 123 has rank 1 and 321 has rank 2)It is known that he uses 6 digit passwords for leisure files, which are his most important files.Q. How many leisure passwords are possible?Correct answer is '2'. Can you explain this answer? tests, examples and also practice CAT tests.
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