# NIACL AO Mains– Quantitative Aptitude Questions Day- 27

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NIACL AO Mains– Quantitative Aptitude Questions Day- 27

maximum of 10 points

Directions (Q. 1 – 5): In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,

a) If x > y

b) If x ≥ y

c) If x < y

d) If x ≤ y

e) If x = y or the relation cannot be established

1)

I) 3x2 – 5x – 42 = 0

II) 4y2 – 8y – 77 = 0

2)

I) 3x – 4y + 7 = 0

II) 2x – 5y = ∛343

3)

I) 3x2 + 18x – 81 = 0

II) 5y2 + 26y + 33 = 0

4)

I) x2 = ∜614656 ÷ 7 + (5/7) of 35 + ∛343

II) y5 = 7776

5)

I) 3x/√x + 4x/√x = x

II) y3 = 117649

Directions (Q. 6 – 10): Study the following information carefully and answer the given questions:

The following table shows the number of mobile phones (in lakhs) manufactured by four different companies in six different years.

6) Total number of mobile phones manufactured by Company C in all the given years is approximately what percentage more/less than the total number of mobile phones manufactured by Company B in all the given years?

a) 24 % less

b) 32 % more

c) 32 % less

d) 24 % more

e) 8 % more

7) If in the year 2018, total manufacturing of Company A, B, C and D be increased by 12 %, 14 %, 18 %, 21 % while comparing with the previous year, then find the total manufacturing of all the given companies together in the year 2018?

a) 13452000

b) 15783000

c) 16894000

d) 14277000

e) None of these

8) Find the ratio between the total manufacturing of company A in the year 2013, 2015, 2016, 2017 together to that of Company D in the year 2012, 2014, 2016, 2017 together?

a) 137: 101

b) 125: 98

c) 113: 87

d) 102: 75

e) None of these

9) The average number of mobile phones manufactured by all the given companies in the year 2014 is approximately what percentage of the average number of mobile phones manufactured by all the given companies in the year 2017?

a) 74 %

b) 83 %

c) 92 %

d) 107 %

e) 94 %

10) Find the difference between the total number of mobile phones manufactured by all the given companies in the year 2012 and 2013 to that of total number of mobile phones manufactured by all the given companies in the year 2015 and 2016 together?

a) 16 lakhs

b) 21 lakhs

c) 13 lakhs

d) 25 lakhs

e) None of these

Directions (Q.1-5):

I) 3x2 – 5x – 42 = 0

3x2 + 9x – 14x – 42 = 0

3x (x + 3) – 14 (x + 3) = 0

(3x – 14) (x + 3) = 0

X = 14/3, -3 = 4.66, -3

II) 4y2 – 8y – 77 = 0

4y2 + 14y – 22y – 77 = 0

2y (2y + 7) – 11(2y + 7) = 0

(2y – 11) (2y + 7) = 0

Y = 11/2, -7/2 = 5.5, -3.5

Can’t be determined

I) 3x – 4y + 7 = 0

3x – 4y = -7 —-> (1)

II) 2x – 5y = ∛343

2x – 5y = 7 —-> (2)

By solving the equation (1) and (2), we get,

X = -9, y = -5

X < y

I) 3x2 + 18x – 81 = 0

3x2 – 9x + 27x – 81 = 0

3x (x – 3) + 27 (x – 3) = 0

(3x + 27) (x – 3) = 0

X = -27/3, 3 = -9, 3

II) 5y2 + 26y + 33 = 0

5y2 + 15y + 11y + 33 = 0

5y (y + 3) + 11 (y + 3) = 0

(5y + 11) (y + 3) = 0

Y = -11/5, -3 = -2.2, -3

Can’t be determined

I) x2 = ∜614656 ÷ 7 + (5/7) of 35 + ∛343

X2 = (28/7) + (5/7)*35 + 7

X2 = 4 + 25 + 7 = 36

X = 6, -6

II) y5 = 7776

Y = (7776)1/5 = 6

X ≤ y

I) 3x/√x + 4x/√x = x

7x/√x = x

√x = 7

X = 49

II) y3 = 117649

Y = ∛117649 = 49

X = y

Directions (Q.6-10):

Total number of mobile phones manufactured by Company C in all the given years

= > 22 + 29 + 18 + 14 + 20 + 27

= > 130 lakhs

Total number of mobile phones manufactured by Company B in all the given years

= > 27 + 26 + 24 + 34 + 23 + 37

= > 171 lakhs

Required % = [(171 – 130)/171]*100 = 23.97 % = 24 % less

In the year 2018, total manufacturing of Company A, B, C and D,

= > 43*(112/100) + 37*(114/100) + 27*(118/100) + 17*(121/100)

= > 48.16 + 42.18 + 31.86 + 20.57

= > 142.77 lakhs = 14277000

The total manufacturing of company A in the year 2013, 2015, 2016, 2017 together

= > 19 + 44 + 31 + 43

= > 137 lakhs

The total manufacturing of company D in the year 2012, 2014, 2016, 2017 together

= > 31 + 25 + 28 + 17

= > 101 lakhs

Required ratio = 137: 101

The average number of mobile phones manufactured by all the given companies in the year 2014

= > (36 + 24 + 18 + 25)/4

= > (103/4) lakhs

The average number of mobile phones manufactured by all the given companies in the year 2017

= > (43 + 37 + 27 + 17)/4

= > (124/4) lakhs

Required % = [(103/4)/ (124/4)]*100 = 83.06 % = 83 %

The total number of mobile phones manufactured by all the given companies in the year 2012 and 2013

= > 35 + 27 + 22 + 31 + 19 + 26 + 29 + 42 = 231 lakhs

The total number of mobile phones manufactured by all the given companies in the year 2015 and 2016

= > 44 + 34 + 14 + 24 + 31 + 23 + 20 + 28 = 218 lakhs

Required difference = 231 – 218 = 13 lakhs

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