Quant Boosters - Sagar Gupta - Set 3


  • Being MBAtious!


    1776^1816! mod 2000
    2000 = 16 * 125
    1776^1816! mod 16 = 0
    Euler of 125 is 100.
    1816! mod 100 = 0.
    1776^1816! mod 125 => 1716^0 mod 125 =1
    16a = 125b + 1
    Remainder = 1376


  • Being MBAtious!


    Q11) In how many ways, 18 identical chocolates can be distributed among 3 identical boxes?


  • Being MBAtious!


    a + b + c = 18 total 20C2 = 190 ways
    when all equal : 1 way
    when 2 equal : 2a + c = 18 -> a = 0 to a = 9 , except a = 6 :
    total 9 ways 3c2 * 9 = 27
    Req cases = (190 - 1 - 3 * 9) / 3! + 1 + 9 = 37


  • Being MBAtious!


    Q12) If the three altitudes in a triangle are 8 cm, 15 cm and 17 cm.which of the following could be the in-radius of the triangle?
    a) 9 cm
    b) 16 cm
    c) 4 cm
    d) none of these


  • Being MBAtious!


    let sides be a,b,c opp to angles A,B,C
    4a = 15b/2 = 17c/2 = k
    we know that : area = inradius * semi perimeter
    semi perimeter =
    ( a + (8a/15) + (8a/17) ) /2 = 511a/510
    inradius = to find
    4a = r * 511a / 510
    r = 510 * 4 / 511 = 2040 / 511 , which is less than 4
    Hence none of these


  • Being MBAtious!


    Q13) Find the number of pairs of x and y if 3x + 7y less than or equal to 210 (x and y are whole numbers)


  • Being MBAtious!


    3x+7y less than equal to 210
    y=0 -> x= 0 to 70
    y=1 -> x= 0 to 67
    y=2 -> x= 0 to 65
    y=3 -> x=0 to 63
    . .
    . .
    y=30 -> x=0
    and so on
    (71 + 68 + 66) + (64 + 61 + 59) + (57 + 54 + 52) + ... 1
    205 + 184 + 163 +142 + 121 + 100 + 79 + 58 + 37 + 16 + 1
    1106


  • Being MBAtious!


    Q14) A bird is sitting on the last coach at the very end of a 100 m long train, travelling at speed of 36 km/ hr. The bird starts flying in the direction of the train at a speed 54 km/hr but rests on the train for 1 s after flying for every 2 s. Find the time taken by the bird to reach the starting of the engine?


  • Being MBAtious!


    100 = 5t
    t = 20 seconds had there been no resting times , the bird would have reached in 20 seconds
    for every 2 seconds , bird takes rest for 1 sec : therefore total time now is 30 sec
    But for the last 2 sec when bird reaches the engine , bird doesn't take rest.. so 30-1 = 29 sec


  • Being MBAtious!


    Q15) A rod of length 30 units is to be cut into P parts so that the magnitude of the product of the lengths of the parts thus obtained is greater than 1 unit. The maximum possible value of P is


  • Being MBAtious!


    30/p , 30/p , 30/p , 30/p , 30/p.........
    (30/p)^p > 1
    p can be max 29


  • Being MBAtious!


    Q16) A and B are running on a circular track of length 3km in the clockwise direction. A laps B in the middle of A's 7th lap. If they are racing on a 100m dash, find the head start that A has to give B so that they finish the race in a dead heat?
    a) 15 (5/13) m
    b) 15 (7/13)m
    c) 17 (2/11)m
    d) None of the above


  • Being MBAtious!


    19.5 = Sa * t
    16.5 = Sb * t
    39 / 33 = Sa / Sb
    100 = 39 * t
    100-x = 33 * t
    100/100-x = 39/33
    x = 200/13 = option A


  • Being MBAtious!


    Q17) Find the number of whole number solutions for A + B + C = 71 where A > B > C


  • Being MBAtious!


    total whole number solutions => 73C2
    73 * 72/2 = 73 * 36
    a = b = c -> 0
    a = b
    2a + b = 71 -> a = 0 to a = 35
    (73 * 36 - 3 * 36)/ 6 = 420


  • Being MBAtious!


    Q18) A 10% solution is one in which 10 gram of solute is dissolved in 100gram of water. On heating the solution water evaporates, so 1 kg of the 10% solution is reduced to 0.4 kg. What is the concentration now?


  • Being MBAtious!


    10 grams sugar : 100 grams water : 110 grams solution
    1000/11 grams sugar : 10000/11 grams water : 1 kg solution
    1000/11 grams sugar : 3400 /11 grams water : 0.4 kg solution
    10 grams sugar in 34 grams water
    10 * 100/34 grams sugar in 100 grams water , which is 29.4


  • Being MBAtious!


    Q19) There were 2 boxes A and B. Box A contained 1000 balls, consecutively numbered from 1 to 1000 such that there was only one number printed on each ball. Box B was initially empty. All the balls on which the number printed was a multiple of 7 were transferred to the box B by Amit. After that all the balls on which the number printed was a multiple of 27 were transferred to the box B by Bineet. Finally, all the balls in the box B on which the number printed was a multiple of 37 were transferred back to the box A by Ishu. The final count of the balls in Box B was :


  • Being MBAtious!


    a : 1000
    b : 0
    a : 1000 - 7k
    b : 7k
    a : 1000 - 7k - 27m
    b : 7k + 27m
    a : 1000 - 7k - 27m + 37n
    b : 7k + 27m - 37n
    142 + 32 - 5 + 1 = 170


  • Being MBAtious!


    Q20) In a 800m race around a stadium having the circumference of 200m the top runner meets the last runner on the 5th minute of the race .If the top runner runs at twice the speed of the last runner,what is the time taken by the top runner to finish the race?
    a) 20 min
    b)15 min
    c)10 min
    d) 5 min


 

Looks like your connection to MBAtious was lost, please wait while we try to reconnect.