Quant Test for IBPS Clerk 2018 Prelim Exam Set – 33

Directions(1-5): Find the relation between x and y and choose a correct option.

  1. 18x^2 – 39x + 20 = 0
    9y^2 – 51y + 52 = 0

    x>=y
    x>y
    y>=x
    y>x
    x=y or relation cannot be established.
    Option C
    18x^2 – 39x + 20 = 0
    =>18x^2 – 15x – 24x + 20 = 0
    => (6x-5)(3x-4) = 0
    => x = 5/6 or 4/3
    9y^2 – 51y + 52 = 0
    => 9y^2 – 12y – 39y + 52 = 0
    => (3y-4)(3y-13) = 0
    => y = 4/3 or 13/3
    y>=x

     

  2. 9x + 4y = 79
    7x – 5y = 29

    x=y or relation cannot be established.
    y>x
    y>=x
    x>y
    x>=y
    Option D
    On equating both the equations.
    X = 7
    y = 4
    x>y

     

  3. X^2 – 35x + 306 = 0
    3y^2 – 23y + 44 = 0

    x>=y
    x>y
    y>=x
    y>x
    x=y or relation cannot be established.
    Option B
    X^2 – 18x – 17x + 306 = 0
    => (x – 17)(x – 18) = 0
    => x = 17 or 18
    3y^2 – 12y – 11y + 44 = 0
    => (y-4)(3y-11) = 0
    => y = 4 or 11/3
    x>y

     

  4. 3x^2 – 37x + 110 = 0
    6y^2 – 40y + 132 = 0

    x=y or relation cannot be established.
    y>=x
    y>x
    x>=y
    x>y
    Option A
    3x^2 – 37x + 110 = 0
    => 3x^2 – 15x – 22x + 110 = 0
    => (3x – 22)(x – 5) = 0
    => x = 5 or 22/3
    6y^2 – 40y + 132 = 0
    => 3y^2 – 18y – 22y + 132 = 0
    => (3y – 22)(y – 6) = 0
    => y = 22/3 or 6
    X=y or no relation can be established.

     

  5. 12x^2 + 13x – 35 = 0
    10y^2 = 21y -9

    x>y
    x=y or relation cannot be established.
    x>=y
    y>=x
    y>x
    Option B
    12x^2 + 13x – 35 = 0
    => 12x^2 + 28x – 15x – 35 = 0 => (3x+7)(4x-5) = 0 => x = -7/3 or 5/4
    10y^2 = 21y -9
    => 10y^2 – 21y + 9 = 0
    => 10y^2 – 15y – 6y + 9 = 0
    => (2y – 3)(5y – 3) = 0
    => y = 3/2 or 3/5
    X=y or relation cannot be established.

     

  6. The length and the breadth of a rectangular plot are in the ratio 5:4. If the cost incurred for fencing the boundary of the plot at Rs. 15 per metre is Rs. 2970. Find the area of the plot.
    2500 m^2
    2420 m^2
    2020 m^2
    2000 m^2
    2520 m^2
    Option B
    Perimeter of the rectangular plot = 2*(5x+4x)
    = 198
    => x = 11m
    Length = 55 m
    Breadth = 44 m
    Area = 55*44 = 2420 m^2

     

  7. A vessel contains mixture of petrol and kerosene in the ratio 5:3 resp. If 16 litres of the mixture is taken out and replaced by 3 litres of kerosene the ratio of petrol to kerosene becomes 3:2 resp. Find the initial quantity of mixture in the vessel.
    62 litres
    80 litres
    75 litres
    88 litres
    90 litres
    Option D
    [5x – 10]/[3x – 6+ 3] =3/2
    => x = 11
    Initial quantity of the mixture = 55+33
    = 88 litres

     

  8. Raj scored 37% marks in an examination but failed by 24 marks. Kiran scored 45% marks in the same examination and got 40 marks above the passing marks. Find the passing marks in the examination.
    280
    295
    320
    333
    300
    Option C
    Let maximum marks be x.
    Passing marks = 37% of x + 24
    Also. Passing marks = 45% of x – 40
    37% of x + 24 = 45% of x – 40
    => x = 800
    Passing marks = 37% of 800 + 24 = 320

     

  9. A train moving with a speed of 54 kmhr. Crosses a pole in 16 seconds. Find the time taken by it to cross a platform 120 m long moving at the same speed.
    18 sec.
    24 sec.
    30 sec.
    22 sec.
    20 sec.
    Option B
    Speed of train in m/s = 54*5/18 =15 m/s
    Length = 15*16 = 240 m
    Time = 240+120/2 = 24 sec.

     

  10. A box contains 20 bulbs out of which 5 are defective. 3 bulbs are randomly taken out of the box. What is the probability that out of the three at least one bulb is defective?
    137/232
    133/228
    131/225
    137/228
    137/221
    Option D
    Probability that atleast one bulb is defective
    = 1 – 15C3/20C3 = 137/228

     


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