Quant Boosters by Shubham Ranka, IIM Calcutta


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    a+b+c+d+e+f = 7 ----- (A)
    a,b,c,d,e,f > 0
    ==> 6c5
    ==> p = 1-6c5/N
    N = no. of solns of (A)
    = 12c5 - x
    x = Ways in which he scores 5 or 7
    For x = 7 ----> 6c1 = 6
    When any of the value is 5
    a'+b'+c'+d'+e'+f' = 7-5 = 2
    7c5
    ==> 1 - 6/ (12c5-6c1-7c5) = 769/775


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    Q 26) P and Q are the two opposite ends of a pond and the distance between them is 420 metres. Messi and Ronaldo start swimming towards each other at the same time from P and Q, with speeds in the ratio 5 : 9 respectively. As soon as any of them reaches an end, he turns back and starts swimming towards the other end. At what distance (in metres) from P will they meet when Ronaldo is in his 13th round?


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    For the same distance, Ratio of time will be inverse of speeds = 9 : 5
    When Ronaldo covers 9 rounds, Messi covers 5.
    ==> When Ronaldo covers 13 , Messi will cover 13 x 5 / 9 = 65/9 rounds.
    ==> Distance = 420 x 65/9 = 9100/3 m
    FOr P, nearest multiple of the track length = 420 x 7 (closest to 65/9 ) = 2960m.
    ==> Distance travelled from P = 9100/3 - 2960 = 43.33m


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    Q27) No of negative integral solution of 7a + 17b + 1000 = 0 is ?


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    a0
    7x + 17y = 1000
    mod 3y/7 = 6
    x y
    138 2
    Tn = 138 + (n-1) * -17 > 0
    n < 9. xx
    ===> 9 solns


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    Q 28) 20% of notes are fake.Probability of accepting a fake for an original is .1 & original never rejected.The probability of accepting original is


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    p(F) = 0.2 | p(O) = 0.8
    p(Acceptance) = 0.8 + 0.2*.1 = .82
    p(Acceptance of Original) = .8/.82 = .97


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    Q 29) There are three classes X, Y and Z. The average age of the students of classes X and Y together is 20 years. The average age of the students of classes Y and Z together is 35 years. The average age of the students of classes X and Z together is 15 years. Which of the following can be the average age of all the three classes together?
    a) 16
    b) 38
    c) 30
    d) 25


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    X+Y = 20(a+b) ----------------------------(1)
    Y+Z=35(b+c) ------------------------------(2)
    X+Z = 15(a+c) ----------------------------(3)
    Let, X+Y+Z/a+b+c = M
    Adding (1), (2) and (3) :
    X+Y+Z = 5(7a+11b+10c)
    = 35(a+b+c) + 5 (4b+3c)
    M = 35 + 5 (4b+3c)/(a+b+c)
    which is greater than 35 ===> (B)


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    Q 30) A hospital nursery has 3 boys and some girls. Overnight a child is born and is added to the group. The next morning, one child is chosen from the group at random, with uniform probability, and turns out to be a boy.Determine the probability p that the overnight addition to the group was also a boy


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    p = prob (overnight born = boy| Next day chosen = boy)
    = prob (overnight born = boy AND Next day chosen = boy) / prob (Next day chosen = boy)
    = .5 * 4/T / (.5*4/T + .5 * 3/T) = 2/3.5 = 4/7 ~ .57


 

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