Quant Test for NIACL AO Prelims Exam Set – 3

Directions(1-5): Compare the values of x and y then choose a required option.

1. 3x – 4(x)^1/2 = 4
   5y = 2(5y)^1/2 + 8
   y>x
   x=<y
   x>y
   x>=y
   x=y or no relation
   Option E
   3x – 4(x)^1/2 = 4
   Squaring on both the side,
   9x^2 – 24x + 16 = 16x
   =>9x^2 – 40x + 16 = 0
   => 9x^2 – 36x – 4x + 16 = 0
   => x = 4,4/9 5y = 2(5y)^1/2 + 8
   Squaring on both the side,
   25y^2 – 80y + 64 = 20y
   => 25y^2 -100y + 64 = 0
   => 25y^2 – 20y – 80y + 64 = 0
   => y = 4/5,16/5
   No relation

    

2. y² – x² = 32
   y – x = 4
   x>=y
   x>y
   x=<y
   y>x
   x=y or no relation
   Option D
   y² – x² = 32
   =>y – x = 4
   =>(y + x) (y – x) = 32
   =>(y + x) 4 = 32
   =>y + x = 8
   y – x = 4
   y = 16 and x = 12
   x < y

    

3. 35x^2 – 13x – 12 = 0
   56y^2 = 53y – 12
   x=<y
   x>=y
   y>x
   x>y
   x=y or no relation
   Option E
   35x^2 – 13x – 12 = 0
   => 35x^2 + 15x – 28x – 12 = 0
   => 5x(7x+3)-4(7x+3) = 0
   => x = (-3/7),4/5
   56y^2 = 53y – 12
   => 56y^2 – 53y + 12 = 0
   => 56y^2 – 21y – 32y + 12 = 0
   => 7y(8y-3) -4(8y-3) = 0
   => y = 4/7,3/8
   No relation

    

4. x² – 31x + 130 = 0
   y² – 53y + 702 = 0
   x>=y
   x=y or no relation
   x=<y
   y>x
   x>y
   Option C
   x² – 31x + 130 = 0
   =>x² – 31x + 130 = 0
   x = 26, 5
   y² – 53y + 702 = 0
   =>y² – 53y + 702 = 0
   =>y = 26, 27
   x ≤ y

    

5. x^2 + 4x = 12
   y^2 – 7y + 10 = 0
   x=y or no relation
   x>y
   y>x
   x=<y
   x>=y
   Option D
   x^2 + 4x = 12
   => x^2 + 4x – 12 = 0
   => x^2 + 6x – 2x – 12 = 0
   => x(x+6) – 2(x+6) = 0
   => (x+6)(x-2) = 0
   => x = -6,2
   y^2 – 7y + 10 = 0
   =>y^2 – 5y -2y + 10 = 0
   => y(y-5)-2(y-5) = 0
   => (y-2)(y-5) = 0
   => y = 2,5
   x=<y

    

Directions(6-10): Answers the questions based on the information given below.

The column graph below shows the production (in quintals) of wheat, rice and maize in five different years.


6. What is the average production of maize in all the years together?
   61.5 quintals
   52.3 quintals
   60.8 quintals
   64.4 quintals
   55.7 quintals
   Option D
   Average production of maize in all the years = (50+63+80+54+75)/5
   = 322/5 = 64.4 quintals

    

7. What is the percentage rise in the production of rice and wheat together in 2014 as compared to 2012?
   17%
   18%
   20%
   10%
   15%
   Option D
   Total production of rice and wheat in 2012 = 75+45 = 120 quintals
   Total production of rice and wheat in 2014 = 62+70 = 132 quintals
   % rise in production = (132-120)/120*100 = 10%

    

8. 60% of the wheat produced in 2014 is exported to Japan and 65% of the wheat produced in 2015 is exported to Japan. Find the difference in the quantity of wheat exported to Japan in 2014 and in 2015?
   6 quintals
   5 quintals
   8 quintals
   4 quintals
   3 quintals
   Option E
   Quantity of wheat exported to Japan in 2014 = 0.6*70
   = 42 quintals
   Quantity of wheat exported to Japan in 2015 = 0.65*60 = 39 quintals
   Required difference = 42 – 39 = 3 quintals

    

9. What is the average production of all the three grains in 2014?
   57 quintals
   55 quintals
   48 quintals
   62 quintals
   60 quintals
   Option D
   Total production of all the three grains in 2014 = 62+70+54
   = 186 quintals
   Average production in 2014 = 186/3 = 62 quintals

    

10. Production of rice in 2016is increased by 25% as compared to previous year and production of rice is increased by 20% in 2017 as compared to previous year. Find the quantity of rice produced in 2017.
    120 quintals
    90 quintals
    115 quintals
    102 quintals
    98 quintals
    Option D
    Production of rice in 2016 = 1.25*68 = 85 quintals
    Production of rice in 2017 = 1.2*85 = 102 quintals