Quant Test for IBPS Clerk 2018 Prelim Exam Set – 17

Directions(1-5): Find the relation between x and y, and choose a correct option.

1. X^2 – 14x + 40 = 0
   y^2 – 25y + 144 = 0
   y>=x
   x>y
   x>=y
   y>x
   x=y or relation cannot be established.
   Option E
   X^2 – 4x – 10x + 40 = 0
   =>x(x-4)- 10(x-4) = 0
   => x = 4,10
   Y^2-25y+144 = 0
   =>y^2 – 16y – 9y + 144 = 0 => y(y-16)-9(y-16)= 0
   => y = 16,9
   x=y or relation cannot be established.

    

2. 12x^2 + 13x – 35 = 0
   10y^2= 21y-9
   x>y
   x>=y
   y>=x
   x=y or relation cannot be established.
   y>x
   Option D
   12x^2 + 13x – 35 = 0
   =>12x^2 + 28x -15x – 35 = 0
   =>4x(3x+7)-5(3x+7)=0
   =>x = -7/3,5/4
   10y^2= 21y-9
   => 10y^2 -15y -6y+ 9 = 0
   => 5y(2y-3)-3(2y-3)=0
   =>y =3/2,3/5
   x=y or relation cannot be established.

    

3. X= (1089)^1/2 – (14^2 – 190)
   y = 13^3 – (45^2+146)
   y>=x
   x>y
   x=y or relation cannot be established.
   y>x
   x>=y
   Option B
   X= (1089)^1/2 – (14^2 – 190)
   => x = 33 – (196-190)
   => x = 27
   y = 13^3 – (45^2+146)
   =>y =2917-(2025+146)
   =>y = 26
   x>y

    

4. 3x+y = 20
   4x+3y = 30
   y>x
   x=y or relation cannot be established.
   y>=x
   x>y
   x>=y
   Option D
   X = 6
   y = 2
   x>y

    

5. X^2 -36x + 323 = 0
   y^2-29y+210 = 0
   x>=y
   x=y or relation cannot be established.
   y>x
   x>y
   y>=x
   Option D
   X^2 -36x + 323 = 0
   => x^2 – 17x – 19x + 323 = 0
   => x(x-17)-19(x-17) = 0
   => x = 17,19
   y^2-29y+210 = 0
   =>y^2 – 15y – 14y + 210 = 0
   => y(y-15)-14(y-15) = 0
   => y = 15,14
   x>y

    

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, the find the area of the plot.
   2550 m^2
   2250 m^2
   2000 m^2
   2420 m^2
   2500 m^2
   Option D
   Perimeter = 2970/15 = 198 m
   Now, 2(5x+4x) = 198
   => x = 11 metres
   Length = 55 m
   Breadth = 44 m
   Required area = 2420 m^2

    

7. A boy cycles from his home to his school with a speed of 12 km/hr. and reaches his school in 45 minutes. If he returns home at a speed of 3 km/hr. more than the speed of going to his school. Find his average speed for the whole journey.
   11.11 km
   12.25 km
   13.33 km
   10.11 km
   9.52 km
   Option C
   Distance between his home and his school = 45/60*12
   = 9 km
   Speed of boy while returning = 12+3 = 15km/hr.
   Time taken to cover the distance between home and school = 9/15 = 0.6 hour
   Required average speed = (9+9)/(0.6+0.75) = 13.33 km

    

8. A man sold an article at 15% discount and earned 36% profit. The discount given on the article was Rs. 576. What should be the selling price if the shopkeeper wanted to earn 42% profit.
   Rs. 3500
   Rs. 4150
   Rs. 3408
   Rs. 3333
   Rs. 3000
   Option C
   Let MP be x. 15% of x = 576 x = (576*100)/15
   => x = Rs. 3840
   SP = 3840-576 = RS.3264
   CP = (3264*100)/136 = Rs.2400
   Required SP = 142% of 2400 = Rs. 3408

    

9. Pipe A fills (1/4)th of the tank in 5 minutes and another pipe B fills (1/5)th of the tank in 6 minutes. Find the time taken to fill half of the tank if both the pipes work together.
   6 minutes
   7 minutes
   9 minutes
   5 minutes
   4 minutes
   Option A
   Time taken by pipe A = 5*4 = 20 minutes
   Time taken by pipe B = 6*5 = 30 minutes
   Let the total capacity of the tank LCM (20 and 30) = 60 units
   Number of units of water filled by A alone in one minute = 3 units
   Number of units of water filled by B alone in one minute = 2 units
   Number of units of water filled by both pipes in one minute = 5 units
   Required time taken by both pipes to fill the tank = 60/(2*5) = 6 minutes

    

10. A bag contains 5 red balls, 3 black balls and 5 white balls. A man draws 3 balls at random from the bag. Find the probability that out of 3 balls at least 2 balls are white.
    40/143
    45/143
    33/143
    45/111
    41/134
    Option B
    Required Probability = [ (5C2*3C1)+(5C2*5C1)+5C3]/13C3
    = 45/143