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