Question Bank - Modern Math - Shashank Prabhu - CAT 100 Percentiler

  • Q15) If n is an integer from 1 to 96 (inclusive), what is the probability for n*(n+1)*(n+2) being divisible by 8?
    a. 25%
    b. 50%
    c. 62.5%
    d. 75%

    [OA: Option c]

  • Q24) Anna has 10 marbles: 5 red, 2 blue, 2 green and 1 yellow. She wants to arrange all of them in a row so that no two adjacent marbles are of the same color and the first and the last marbles are of different colours. How many different arrangements are possible?
    a. 30
    b. 60
    c. 120
    d. 240

    [OA: Option b]

  • Q25) The year 1789 has three and no more than three adjacent digits (7, 8 and 9) which are consecutive integers in increasing order. How many years between 1000 and 9999 have this property?

    1. 130
    2. 142
    3. 151
    4. 169

    [OA: Option 1]

  • Q32) Players from only two countries Dakistan and Pagladesh participated in a Ludo tournament. Each game of the tournament involved 3 players with no two games having the same set of 3 players. The number of games involving only Dakistani players was 455 and the number of games involving only Pagladeshi players was 120. If the total number of games played in the tournament was maximum possible, then how many games involved at least one player each from Dakistan and Pagladesh?

    [OA: 1725]

  • Q36) While adding all the page numbers of a book, I found the sum to be 1000. But then I realized that two page numbers (not necessarily consecutive) have not been counted. How many different pairs of two page numbers can be there?

    [OA: 23]

  • Q40) India fielded n (> 3) bowlers in a test match and they operated in pairs.if a particular bowler did not how in pair with at least two other bowlers, then at most how many bowlers could have bowled in pair with every other bowler in the team?

    [OA : n - 3]

  • Q43) How many sequences of 1's and 2's sum to 15?

    [OA: 987]

  • Q52) Four different digits are chosen and all possible positive four-digit numbers of distinct digits are constructed out of them. The sum of the four-digit numbers is 186648. How many different sets of such four digits can be chosen?

    [OA: 2]

  • Q60) In a group of people, there are 19 who like apples, 13 who like bananas, 17 who like cherries, and 4 who like dates. (A person can like more than 1 kind of fruit.) Each person who likes bananas also likes exactly one of apples and cherries. Each person who likes cherries also likes exactly one of bananas and dates. Find the minimum possible number of people in the group.

    [OA : 32]

  • Q91) A four-letter code has to be formed using the alphabets from the set (a, b, c, d) such that the codes formed have odd number of a’s. How many different codes can be formed satisfying the mentioned criteria?

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