# 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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