Mixed Quantitative Aptitude Questions Set 167

Directions(1-5): Find the values of x and y, compare and choose a correct option.

  1. I.x^2 – 32x + 252 = 0
    II.y^2 – 26y + 168 = 0
    y >= x
    x > y
    y > x
    x >= y
    No relation
    Option D
    I.x^2 – 32x + 252 = 0
    =>x^2 – 18x -14x + 252 = 0
    =>(x-14)(x-18) = 0
    =>x = 14,18
    II.y^2 – 26y + 168 = 0
    =>y^2 -12y -14y +168 = 0
    =>(y-12)(y-14) = 0
    =>y = 12,14
    x >= y

     

  2. I.x^2 + 42x + 441 = 0
    II.y^2 + 34y + 289 = 0
    x > y
    x >= y
    y >= x
    y > x
    No relation
    Option D
    I.x^2 + 42x + 441 = 0
    =>x^2 + 21x + 21x+ 441 = 0
    =>(x+21)(x+21) = 0
    =>x = -21,-21
    II.y^2 + 34y + 289 = 0
    =>y^2 + 17y + 17y + 289 = 0
    =>(y+17)(y+17) = 0
    =>y = -17,-17
    y > x

     

  3. I.x^2 + 26x + 165 = 0
    II.y^2 + 30y + 209 = 0
    x > y
    y > x
    x >= y
    y >= x
    No relation
    Option E
    I.x^2 + 26x + 165 = 0
    =>x^2 + 15x +11x + 165 = 0
    =>(x+15)(x+11) = 0
    =>x = -15,-11
    II.y^2 + 30y + 209 = 0
    =>y^2 + 19y +11y + 209 = 0
    =>(y+19)(y+11) = 0
    =>y = -19,-11
    No relation

     

  4. I.3x^2 + 19x -14 = 0
    II.3y^2 – 31y + 36 = 0
    y >= x
    y > x
    x > y
    x >= y
    No relation
    Option B
    I.3x^2 + 19x -14 = 0
    =>3x^2 -2x + 21x – 14 = 0
    =>(x+7)(3x -2) = 0
    =>x = -7,2/3
    II.3y^2 – 31y + 36 = 0
    =>3y^2 -4Y -27Y +36 = 0
    =>(y-9)(3y -4 ) = 0
    =>y = 9,4/3
    y > x

     

  5. I.x^2 + 4x – 221 = 0
    II.y^2 – 4y – 221= 0
    x >= y
    y > x
    x > y
    No relation
    y >= x
    Option D
    I.x^2 + 4x – 221 = 0
    =>x^2 – 13x + 17x – 221 = 0
    =>(x+17)(x-13) = 0
    =>x = -17,13
    II.y^2 – 4y – 221= 0
    =>y^2 – 17 y + 13y – 221 = 0
    =>(y-17)(y-13) = 0
    =>y = -13,17
    No relation

     

  6. Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
    4
    8
    6
    5
    3
    Option C
    [x(x+6)]/[x+x+6]=4
    =>x^2+6x=8x+24
    =>x^2−2x−24=0
    =>(x−6)(x+4)=0
    =>x= 6

     

  7. A train, having a length of 110 metre is running at a speed of 60 kmph. In what time, it will pass a man who is running at 66 kmph in the direction opposite to that of the train.
    8
    4
    7
    6
    5
    Option D
    Distance =110 metre
    Since train and man move in opposite directions, relative speed
    =(60+6)=66 km/hr
    =66×5/18 m/s=110/6 m/s
    Time =110/(110/6) = 6 seconds

     

  8. A train 108 metre long is moving at a speed of 50 km/hr. It crosses a train 112 metre long coming from opposite direction in 6 seconds. What is the speed of the second train?
    89 km/hr.
    78 km/hr.
    66 km/hr.
    70 km/hr.
    82 km/hr.
    Option E
    Distance covered =(108+112)=220 metre
    Time =6 seconds
    Relative speed =220/6=110/3 m/s
    =110/3×18/5=132 km/hr.
    50 + Speed of second train =132 km/hr.
    Speed of second train =(132−50)= 82 km/hr.

     

  9. On my brother’s 15th birthday, his height was 159 cm, having grown 6% since the year before. How tall was he in the previous year?
    140 cm
    150 cm
    120 cm
    130 cm
    160 cm
    Option B
    Height in the previous year
    =(159×100)/106 =150 cm

     

  10. In how many ways can 7 different balls be distributed in 5 different boxes if box 3 and box 5 can contain only one and two number of balls respectively and rest of the boxes can contain any number of balls?
    8520
    8448
    8180
    8000
    8505
    Option E
    Required number of ways
    = 7C1 × 6C2 ×3^4
    =7×15×81= 8505

     


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