# 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
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