Quant Test for LIC AAO Prelims Exam Set – 9

Directions(1-5): Compare both the equations and choose a correct option.

  1. I.12x^2 – 13x + 3 = 0
    II.2y^2 + 7y – 4 = 0

    y >= x
    x > y
    No relation
    y > x
    x >= y
    Option C
    I.12x^2 – 13x + 3 = 0
    =>12x^2 – 9x – 4x + 3 = 0
    =>(4x-3)(3x – 1) = 0
    =>x = 1/3,3/4
    II.2y^2 + 7y – 4 = 0
    =>2y^2 + 8y – y – 4 = 0
    =>(2y-1)(y+4) = 0
    =>y = -4,1/2
    No relation.

     

  2. I.4x + 7y = 209
    II.12x – 14y = – 38

    x >= y
    x > y
    y > x
    y >= x
    No relation
    Option E
    On solving both the equations, we get
    x=y = 19
    No relation.

     

  3. I.9x^2 – 45x + 56 =0
    II. 4y^2 – 17y + 18 = 0

    y >= x
    No relation
    x >= y
    y > x
    x > y
    Option E
    I.9x^2 – 45x + 56 =0
    =>9x^2 – 24x – 21x + 56 = 0
    =>(3x – 8)(3x- 7) = 0
    =>x = 8/3,7/3
    II. 4y^2 – 17y + 18 = 0
    =>4y^2 – 8y – 9y + 18 = 0
    =>(y-2)(4y-9) = 0
    =>y = 2,9/4
    x>y

     

  4. I.9x^2 -36x + 35 = 0
    II.2y^2 – 15y – 17 = 0

    No relation
    x >= y
    x > y
    y > x
    y >= x
    Option A
    I.9x^2 -36x + 35 = 0
    =>9x^2 – 21x – 15x + 35 = 0
    =>(3x- 7)(3x – 5)= 0
    =>x = 5/3,7/3
    II.2y^2 – 15y – 17 = 0
    =>2y^2 – 17y + 2y – 17 =0
    =>(y+1)(2y – 17)= 0
    =>y = -1,17/2
    No relation.

     

  5. I.x^2 – 11x + 24 = 0
    II.6y^2 – 101y + 425 =0

    y > x
    y >= x
    x > y
    No relation
    x >= y
    Option A
    I.x^2 – 11x + 24 = 0
    =>x^2 – 3x – 8x + 24 = 0
    =>(x-3)(x-8) = 0
    =>x = 3,8
    II.6y^2 – 101y + 425 =0
    =>6y^2 – 50y – 51y + 425 = 0
    =>(2y – 17)(3y – 25) = 0
    =>y = 17/2,25/3
    y > x

     

  6. A fresh fruit contains 80% of water, when it is placed in sunlight after sometime it contains only 25% of water and now its weight is 44 kg. Find the weight o fresh fruit?
    152 kg
    170 kg
    165 kg
    136 kg
    142 kg
    Option C
    Water : pulp
    Fresh
    => 4:1
    Fry
    =>1:3
    Multiply ratio of fresh fruit by 3 and 4 unit of dry fruit is 44 kg.
    1 unit -> 11 kg
    Fresh fruit = 11*15 = 165 kg

     

  7. A solution containing 45 ml of acid and 60 ml of water is completely mixed with another solution E, which contains 7/11 of acid. If the proportion of acid and water in the final mixture is equal, find the quantity of solution E.
    68 ml
    70 ml
    55 ml
    40 ml
    62 ml
    Option C
    Let the quantity of solution E be x ml.
    Amount of acid in final mixture = (45 + 7x/11) ml
    Amount of water in final mixture = (60+4x/11) ml
    Now, (45 + 7x/11) = (60+4x/11)
    =>x = 55 ml

     

  8. A boat can cover 36 km in still water and the same distance downstream, in 4 hours and 3 hours resp. Find the time taken by the boat to cover 21 km upstream and 48km downstream.
    3 hours 10 minutes
    4 hours 20 minutes
    7 hours 30 minutes
    6 hours 15 minutes
    5 hours 40 minutes
    Option C
    Speed of boat in still water = 36/4 = 9 km/hr.
    Downstream speed = 36/3 = 12 km/hr.
    Speed of the stream = 24 – 18 = 3 km/hr.
    Upstream speed of the boat = 9-3 = 6 km/hr.
    Time taken = 21/6 + 48/12 = 7 hours 30 minutes

     

  9. A,B and C together started a business with initial investments of Rs.4500, Rs.6000 and Rs. 7500 resp. In this business, A is the main working partner for which he gets 16% of the profit to supervise the business, and rest of the profit is shared among them in the ratio of their investments. Find the profit share of A out of the total profit of Rs.5400.
    Rs.1662
    Rs.1998
    Rs.1850
    Rs.1998
    Rs.1880
    Option D
    Respective ratio = 4500:6000:7500 = 3:4:5
    Profit of A for being a working partner = 0.16*5400 = Rs.864
    Profit of A for his investment = (5400- 864)*3/12 = Rs.1134
    Total profit share of A = 864+ 1134 = Rs.1998

     

  10. A baseball team of 9 players is to be selected from a group of 7 male players and 6 female players. In how many ways a team having at most four female players is selected?
    477 ways
    550 ways
    320 ways
    400 ways
    470 ways
    Option E
    Total number of ways = 6C4*7C5 + 6C3*7C6 + 6C2*7C7
    = 315+140+15 = 470 ways

     


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