DILR Sets (with Video solutions) - Shashank Prabhu, CAT 100 Percentiler - Part 7

  • Set 19

    Dominic Cobb has pooled in his life’s savings into a super-secret account at Gringotts with encrypted numerical passwords. However, he is not too good at basic logic and reasoning and so, his passwords are crack-able. 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.

    To remember which password he is using, Cobb 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.

    It is known that he uses 6 digit passwords for safeguarding his browsing history, and these are the ones dearest to him and hence, the most important.

    1. What is the sum of all possible values of the fourth digit of the password that he uses for safeguarding his browsing history?

    2. How many passwords can be used to safeguard his browsing history?

    3. What is the difference between the last two passwords that he uses to safeguard his most important data?

    4. What is the number of five digit passwords that can he use?

    Video solution:

    Set 20

    P. C. Sorkar, the master magician from India of international repute once placed 52 playing cards on his table. Sheldon Cooper, the first of His name, Protector of the Spot was learning to shuffle the cards to learn the magic that his friend Howard had refused to teach him and started studying the patterns if he shuffled the deck in a particular manner. Initially the topmost card was picked and put back into the deck again so as to occupy the 27th place from the bottom. After this the lower most card was drawn out and inserted back into the deck so as to occupy the 26th place from the top. This set of two operations constituted what he called a shuffling.

    1. The top card will be at what position after 17th shuffling?
      a. 42nd from the top
      b. 10th from the bottom
      c. 42nd from the bottom
      d. 10th from the top

    2. After how many shufflings will third card from the top come back to its original position?
      a. 26
      b. 29
      c. 52
      d. 55

    3. What can we say about the positions of playing cards after first 26 shufflings?
      a. The card that was initially at the top of the deck will be immediately next to the card that was initially at the bottom of the deck.
      b. The top 26 cards will become the bottom 26 cards, in the same order.
      c. The bottom 26 cards will become the top 26 cards, in the reverse order.
      d. None of the above

    Video Solution:

    Set 21

    Two players X and Y are playing a game of coins. Any player can pick 2, 3, 4, 5 or six coins in his turn. The player who picks the last coin always wins. If per chance their remains one coin for a person before his turn, then the game ends in a draw. While answering every question you will assume that each person is rational, intelligent and will always try to win the game.

    1. If there are 70 coins in all and X starts the game, what should he pick in order to ensure a win always?
      a. 6
      b. 2
      c. 4
      d. He can never win

    2. If Y starts the game and there are 32 coins. What should he pick in order to ensure win, irrespective of whatever strategy X applies?
      a. 4
      b. 6
      c. 3
      d. He can never win

    3. If there are 30 coins and its X’s turn, how many different possible number of coins he can pick so that he does not lose the game?
      a. 1
      b. 2
      c. 3
      d. 4

    Video Solution

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