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