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[WpProQuiz 7294]Quadratic Equations
Directions (1 – 5): Following question contains two equations as I and II. You have to solve both equations and determine the relationship between them and give answer as,
a) If x > y
b) If x ≥ y
c) If x = y or relationship cannot be determined
d) If x < y
e) If x ≤ y
1)
I) x2 + 12x + 20 = 0
II) y2 + 13y + 22 = 0
2)
I) x2 + 23x + 120 = 0
II) y2 + 13y + 42 = 0
3)
I) x2 – 21x + 90 = 0
II) y2 – y –20 = 0
4)
I) x2 – 2x – 48 = 0
II) y2 + 14y + 48 = 0
5)
I) x2 + 234 = 718
II) y2 = √484
Caselet
Directions (6 – 10): Study the following information carefully and answer the questions given below.
In company A, the ratio of number of employees in IT, HR and Sales department is 5: 4: 7. The ratio of the number of employees in Sales to IT department from B is 9: 5. Total number of employees from A is 50% of the total number of employees from B and the number of IT employees from B is 140. The ratio of number of sales department employees from A to B is 1: 2.
6) What is the difference between the number of HR department employees from A and B?
a) 110
b) 112
c) 115
d) 118
e) None of these
7) What is the total number of employees from A?
a) 288
b) 292
c) 312
d) 310
e) None of these
8) The number of Sales department employees from B is approximately what percent of the total number of employees from B?
a) 43.75%
b) 42.80%
c) 41.85%
d) 40.50%
e) None of these
9) What is the ratio of the number of IT employees from A to B?
a) 11: 7
b) 9: 14
c) 5: 7
d) 1: 2
e) None of these
10) What is the difference between the total number of sales department employees from A and B together and the total number of HR department employees from A and B together?
a) 122
b) 128
c) 132
d) 138
e) None of these
Answers :
Directions (1-5) :
1) Answer: c)
x2 + 12x + 20 = 0
x2 + 10x + 2x + 20 = 0
x(x + 10) + 2(x + 10) = 0
(x + 2)(x + 10) = 0
x= -2, -10
y2 + 13y + 22 = 0
y2 + 11y + 2y + 22 = 0
y(y + 11) + 2(y + 11) = 0
(y + 2)(y + 11) = 0
y = -2, -11
Relationship between x and y cannot be established.
2) Answer: d)
x2 + 23x + 120 = 0
x2 + 8x + 15x + 120 = 0
x(x + 8) + 15(x + 8) = 0
(x + 15)(x + 8) = 0
x = -15, -8
y2 + 13y + 42 = 0
y2 + 7y + 6y + 42 = 0
y(y + 7) + 6(y + 7) = 0
(y + 6)(y + 7) = 0
y = -6, -7
Hence x < y
3) Answer: a)
x2 – 21x + 90 = 0
x2 – 15x – 6x + 90 = 0
x(x – 15) – 6(x – 15) = 0
(x – 6)(x – 15) = 0
x = 6, 15
y2 – y – 20 = 0
y2 – 5y + 4y – 20 = 0
y(y – 5) + 4(y – 5) = 0
(y + 4)(y – 5) = 0
y = -4, 5
Hence x > y
4) Answer: b)
x2 – 2x – 48 = 0
x2 – 8x + 6x – 48 = 0
x(x – 8) + 6(x – 8) = 0
(x + 6)(x – 8) = 0
x = -6, 8
y2 +14y + 48 = 0
y2 + 8y + 6y + 48 = 0
y(y + 8) + 6(y + 8) = 0
(y + 6)(y + 8) = 0
y = -6, -8
Hence x ≥ y
5) Answer: e)
x2 + 234 = 718
x2 = 718 – 234 = 484
x = -22, 22
y2 = √484
y = 22
Hence x ≤ y
Directions (6 – 10):
Number of IT department employees from B = 140
Number of sales department employees from B = 9/5 * 140 = 252
Number of sales department employees from A = ½ * 252 = 126
Number of IT department employees from A = 5/7 * 126 = 90
Number of HR department employees from A = 4/7 * 126 = 72
Total number of employees from A = 126 + 90 + 72 = 288
Total number of employees from B = 100/50 * 288 = 576
Number of HR department employees from B = 576 – 140 – 252 = 184
6) Answer: b)
Difference = 184 – 72 = 112
7) Answer: a)
Total number of employees from A = 126 + 90 + 72 = 288
8) Answer: a)
Number of sales department employees from B = (9/5) * 140 = 252
Total number of employees from B = (100/50) * 288 = 576
Required percentage = (252/576) * 100 = 43.75%
9) Answer: b)
Number of IT department employees from B = 140
Number of IT department employees from A = 5/7 * 126 = 90
Required ratio = 90: 140
=9: 14
10) Answer: a)
Number of sales department employees from B = 9/5 * 140 = 252
Number of sales department employees from A = ½ * 252 = 126
Number of HR department employees from B = 576 – 140 – 252 = 184
Number of HR department employees from A = 4/7 * 126 = 72
Required ratio = (252 + 126) – (184 + 72)
= 122
