# Quant Test for LIC AAO Prelims Exam Set – 23

Directions(1-5):
Compare the value of x and y and choose a correct option.

1. I. 12x^2 – 40x + 32 = 0
II.8y^2 – 40y + 48 = 0

y>x
x>=y
x > y
y>=x
Can’t be determined
Option D
I. 12x^2 – 40x + 32 = 0
12x^2 – 24x – 16x + 32 = 0
12x(x – 2) – 16(x – 2) = 0
(12x – 16) (x – 2) = 0
x = 16/12, 2 = 1.33, 2
II.8y^2 – 40y + 48 = 0
8y^2 – 16y – 24y + 48 = 0
8y(y – 2) – 24(y – 2) = 0
(8y – 24) (y – 2) = 0
y = 3, 2
y>=x

2. I. 5x^2 + 3x -14 = 0
II. 5y^2 + 8y – 21 = 0

x > y
x>=y
y>=x
Can’t be determined
y>x
Option D
I. 5x^2 + 3x -14 = 0
5x^2 + 10x – 7x -14 = 0
5x(x + 2) – 7(x+ 2) = 0
(5x – 7) (x + 2) = 0
x = 7/5, -2
II. 5y^2 + 8y – 21 = 0
5y^2 + 15y – 7y – 21 = 0
5y(y + 3) – 7(y + 3) = 0
(5y – 7) (y + 3) = 0
y = 7/5, -3
Can’t be determined

3. I. 2x^2 + 12x + 16 = 0
II. 3y^2 -7y – 6 = 0

Can’t be determined
y>=x
x > y
x>=y
y>x
Option E
I. 2x^2 + 12x + 16 = 0
2x^2 + 4x + 8x + 16 = 0
2x(x + 2) + 8(x + 2) = 0
(2x + 8)(x + 2) = 0
x = -4, -2
II. 3y^2 -7y – 6 = 0
3y^2 -9y + 2y – 6 = 0
3y(y – 3) + 2(y – 3) = 0
(3y + 2) (y – 3) = 0
y = – 2/3, 3 = -0.667, 3
y > x

4. I.4x – 5y = 28
II.3x + 4y = -10

y>x
Can’t be determined
x>=y
x > y
y>=x
Option D
I.4x – 5y = 28
II.3x + 4y = -10
By solving the equation (1) and (2),
x = 2, y = – 4
x > y

5. I. 3x^2 +14x +15 = 0
II. 3y^2 -13y +14 = 0

y>=x
x>=y
Can’t be determined
y>x
x > y
Option D
I. 3x^2 +14x +15 = 0
3x^2 +9x + 5x + 15 = 0
3x(x+3) + 5(x+3) = 0
(3x+5) (x+3) = 0
x= -5/3, -3
II. 3y^2 -13y +14 = 0
3y^2 – 6y – 7y +14 = 0
3y(y-2)-7 (y-2) = 0
(3y-7)(y – 2) = 0
yY= 7/3, 2
y>x

6. The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat in still water?
30
25
22
27
24
Option C
Let the speed of the boat in still water = x km/hr
Speed of the current = 2 km/hr
speed downstream = (x+2) km/hr
speed upstream = (x−2) km/hr
10/(x−2)+10/(x+2) = 11/12
=>11x^2−240x−44 = 0
=>11x^2−242x+2x−44 = 0
=>11x(x−22)+2(x−22) = 0
=>(x−22)(11x+2)=0
x = 22 or −2/11

7. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
5/9
6/13
3/10
5/8
6/11
Option E
Part of the tank filled by pipe A in 1 minute =130
Part of the tank filled by pipe B in 1 minute =120
Part of the tank filled by pipe C in 1 minute =110
Part of the tank filled by pipe C in 3 minutes =3×1/10=3/10
Part of the tank filled by pipe A,B,C together in 1 minute =130+120+110=1160
Part of the tank filled by pipe A,B,C together in 3 minute =3×1160=1120
Required proportion =(3/10)/(11/20) = 6/11

8. Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
2780
2550
2420
2350
2140
Option C
Speed of sound =1100=1100 ft/s
Time =11/5 second
Dist. =1100×11/5=220×11= 2420 ft

9. A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B’s share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
7900
6900
7500
8200
7170
Option C
A : B : C =20000×24:15000×24:20000×18
=20×4:15×4:20×3
=4×4:3×4:4×3=4:3:3
B’s share = 25000×3/10=7500

10. There are 5 yellow, 4 green and 3 black balls in a bag. All the 12 balls are drawn one by one and arranged in a row. Find out the number of different arrangements possible.
22570
24540
26890
27720
22580
Option D
Required number of arrangements =12!/5!* 4! *3!
= 27720