# 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

6. 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.

7. 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

8. 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%

9. 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

10. 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

11. 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

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