Question Bank (2) - Quant Mixed Bag - Shashank Prabhu, CAT 100 Percentiler


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Number of Questions
    Topic - Quant Mixed Bag
    Answer Key Available ? : Yes
    Source : Learningroots forum


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q1) Instead of dividing Rs. 180 among A, B and C in the ratio (1/3) : (1/4) : (1/6) respectively, it was divided in the ratio 3 : 4 : 6 by mistake. Who gained in this transaction?
    [OA: C]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q2) J and K sit in a circular arrangement along with 10 other people. What is the probability that they will sit together?
    [OA: 2/11]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q3) Hiccup was the guest speaker at a seminar on “How to train your dragon” at the Romanian Dragon Sanctuary. He left his office and traveled at a certain speed so that he would reach the Sanctuary on time. After travelling half the distance, he realised that he had left his laptop at his office. He turned back immediately and increased his speed by 50% and reached his office. As compared to his original speed, by what percent should Hiccup increase his speed so that he still reaches the Sanctuary on time?
    [OA: 500%]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q4) How many numbers greater than 13000 can be formed using the digits 5, 0, 8, 1 and 7 such that each digit is used exactly once?
    [OA: 90]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q5) A man works in a building located 7 blocks east and 8 blocks north of his home. He reaches his office and then walks to a supermarket located 2 blocks east and 4 blocks north of his home. If all the streets in the rectangular pattern are available to him for walking and he always takes the shortest route, how many different routes can he take to go from his house to the supermarket via his office?
    [OA: 15C7 * 9C4]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q6) How many three digit numbers are of the form xyz with x < y, z < y and x ≠ 0?
    [OA: 240]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q7) If 9x + 15xy + 35y = 100, for all real x, y > 0, then find the minimum value of 3x + 5y.
    [OA: 12]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Hint: 3x(3+5y)+7(3+5y)=121
    (3x+7)(3+5y)=121
    Apply either equal terms logic or AM>=GM


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q8) The probability that a builder will get a construction contract is 3/4 and the probability that he will not get the electrical contract is 7/9. If the probability of getting at least one contract is 5/6, what is the probability that he will get both?
    [OA: 5/36]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    P(getting an electrical contract) = 2/9
    So, using basic set theory, 5/6 = 3/4 + 2/9 - P(both)
    P(both) = 5/36


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q9) There are 4 members in a committee. If one of them is replaced by a younger member such that the average age of the committee is as it was 6 years ago. The new member is how many years younger than the member replaced?
    [OA: 24]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q10) Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A and R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?
    [OA: 7.5 hours]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Take the capacity of tank A to be 120 units.
    Find out work done per hour by P, Q and R and then use the cumulative work to find out the total time.


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q11) A + 2B + 3C + 4D = 36, where A, B, C and D are positive integers. What is the maximum value of A * (B^2) * C * (D^2)?
    [OA: 3888]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Take the numbers as a, b, b, 3c, 2d, 2d and apply AM >= GM.
    (a + b + b + 3c + 2d + 2d)/6 >= (a * b * b * 3c * 2d * 2d)^1/6
    6^6 >= 12 * a * b^2 * c * d^2
    a * b^2 * c * d^2 =< 3888


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q12) A box contains 11 cards. Each card has a number from 1 to 11 (both inclusive) and each number is used exactly once. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?
    [OA: 2/33]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    For the median to be 3, there have to be 2 numbers less than 3 and two greater than 3. 1 and 2 are automatic choices and so, the other two numbers can be selected from the remaining 8 in 8c2 = 28 ways. Total ways is 11c5 = 462. Probability will be 14/231 or 2/33.


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q13) Number of integer solution of the equation a^12 + 12 = b^4
    [OA: 4]


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    (2,-2), (2,2), (-2,-2) and (-2,2)


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