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[WpProQuiz 7324]Quadratic Equations
Directions (Q. 1 – 5): In each of these 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 no relation can be established between x and y
1) I) x = √(12875 – 3271)
II) y = ∛474552
2) I) x2 – 6x – 72 = 0
II) y2 + 3y – 88 = 0
3) I) 3x2 + 26x + 56 = 0
II) 2y2 + 15y + 28 = 0
4) I) 4x – 5y = -12
II) 3x + 4y = 53
5) I) x2 – 17x + 52 = 0
II) y2-5y – 66 = 0
Data interpretation
Directions (Q. 6 – 10) Study the following information carefully and answer the given questions.
The following table shows the total number of tyres (In lakhs) manufactured by 5 different companies in a certain year.
6) Total number of tyres rejected by the company P is approximately what percentage more/less than the total number of tyres rejected by the company T?
a) 7 % less
b) 15 % more
c) 15 % less
d) 24 % more
e) 7 % more
7) Find the average number of tyres manufactured by all the given companies together?
a) 32.4 lakhs
b) 28.5 lakhs
c) 30.8 lakhs
d) 34.6 lakhs
e) None of these
8) Find the difference between the total number of tyres sold by the company Q to that of company S?
a) 792600
b) 756800
c) 833200
d) 809270
e) None of these
9) Find the ratio between the total number of tyres rejected by the company Q to that of R?
a) 72: 55
b) 53: 115
c) 84: 137
d) 65: 96
e) None of these
10) Total number of tyres sold by the company P is approximately what percentage of total number of tyres sold by the company R?
a) 60 %
b) 75 %
c) 50 %
d) 85 %
e) 105 %
Answers:
Directions (1-5):
1) Answer: a)
I) x = √(12875 – 3271)
X = √9604 = 98
II) y = ∛474552
Y = 78
X > y
2) Answer: e)
I) x2 – 6x – 72 = 0
(x – 12) (x + 6) = 0
X = 12, – 6
II) y2 + 3y – 88 = 0
(y + 11) (y – 8) = 0
Y = -11, 8
Can’t be determined
3) Answer: d)
I) 3x2 + 26x + 56 = 0
3x2 + 12x + 14x + 56 = 0
3x(x + 4) + 14(x + 4) = 0
(3x + 14) (x + 4) = 0
X = -14/3, -4 = -4.667, -4
II) 2y2 + 15y + 28 = 0
2y2 + 8y + 7y + 28 = 0
2y(y + 4) + 7 (y + 4) = 0
(2y + 7) (y + 4) = 0
Y = -7/2, -4 = -3.5, -4
X ≤ y
4) Answer: c)
4x – 5y = -12 –> (1)
3x + 4y = 53 –> (2)
By solving the equation (1) and (2), we get,
X = 7, y = 8
X < y
5) Answer: e)
I) x2 – 17x + 52 = 0
(x -14) (x – 3) = 0
X = 14, 3
II) y2 – 5y – 66 = 0
(y – 11) (y + 6) = 0
Y = 11, -6
Can’t be determined
Directions (6-10):
6) Answer: e)
Total number of tyres rejected by the company P
= > 3200000*(2/100) = 64000
Total number of tyres rejected by the company T
= > 4000000*(1.5/100) = 60000
Required % = [(64000 – 60000)/60000]*100 = 7 % more
7) Answer: a)
The average number of tyres manufactured by all the given companies together
= > (32 + 26 + 48 + 16 + 40)/5
= > 162/5 = 32.4 lakhs
8) Answer: c)
The total number of tyres sold by the company Q
= >2600000*(95/100)*(84/100) = 2074800
The total number of tyres sold by the company S
= > 1600000*(97/100)*(80/100) = 1241600
Required difference = 2074800 – 1241600 = 833200
9) Answer: d)
The total number of tyres rejected by the company Q
= > 26*(5/100) = 1.3 lakhs
The total number of tyres rejected by the company R
= > 48*(4/100) = 1.92 lakhs
Required ratio = 1.3: 1.92 = 130: 192 = 65: 96
10) Answer: b)
Total number of tyres sold by the company P
= > 3200000*(98/100)*(78/100) = 2446080
Total number of tyres sold by the company R
= > 4800000*(96/100)*(72/100) = 3317760
Required % = (2446080/3317760)*100 = 73.726 = 75 %
