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Quadratic Equation
Directions (1 – 5): In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the relation between x and y 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 relationship between x and y cannot be determined.Â
1) I) 3x2 + 23x + 42 = 0
II) y2 + 4y – 21 = 0
2) I) 14x2 – 132x + 238 = 0
II) 4y2 – 17y + 13 = 0
3) I) 5x2 – 19x + 12 = 0
II) 3y2 + 14y + 15 = 0
4) I) 4x2 + 3x – 10 = 0
II) y2 – (343)1/3 – √841 = 0
5) I) 6x2 – 25x + 24 = 0
II) 5y2 + 27y + 10 = 0
Data Sufficiency
Directions (6 – 10): In each of the following questions, a question is followed by three statements I, II and III. Read all the statements to find the answer to given question and then answer accordingly that which statement/s can give the answer alone/together.
6) Find the share of Aman in the profit after three years?
I) Aman, Sunil and Kabir entered into a partnership for three years and at the end of three years they earned a profit of Rs.200000.
II) Ratio of investment amount of Aman, Sunil and Kabir is 3:5:4 respectively.
III) At the end of two years, Kabir doubled his investment.
a) Only I and III
b) Only II
c) Only II and III
d) All I, II and III
e) None is sufficient
7) Find the distance travelled by the train in 9 hours?
I) Ratio of the speed of the train, bus and car is 8:2:3.
II) The car can travel a distance of 216 km in 8 hours.
III) The bus can travel a distance of 24 km in 2 hours.
a) All I, II and III
b) Only I
c) Only II
d) Only I and Either II or III
e) None is sufficient
8) Find the probability of drawing one blue ball from the bag?
I) Probability of drawing one red ball from the bag is 1/3
II) The bag contains 4 red, 3 green and some blue balls.
III) Number of blue balls is less than number of red balls.
a) Only I and III
b) Only II and III
c) Only I and II
d) All I, II and III
e) None is sufficient
9) Find the age of Mauli after ten years?
I) Ratio of the present ages of Mauli and Nandini is 5:4 respectively.
II) Ratio of the ages of Mauli and Nandini before five years was 4:3 respectively.
III) Ratio of the ages of Mauli and Nandini after ten years will be 7:6 respectively.
a) All I, II and III
b) Any two of the three
c) Only II
d) Only III
e) None is sufficient
10) Find the present age of Kumud?
I) Average age of Roshni, Sitara, Kumud and Mini before four years was 26 years.
II) Average of the present ages of Roshni and Sitara is 31 years.
III) Kumud is two years older than Mini.
a) Only I and III
b) Only II
c) Only II and III
d) All I, II and III
e) None is sufficient
Answers:
Directions (1-5) :
1) Answer: e)
I) 3x2 + 23x + 42 = 0
=> (3x + 14)(x + 3) = 0
=> x = -14/3, -3
II) y2 + 4y – 21 = 0
=> (y – 3)(y + 7) = 0
=> y = 3, -7
Hence, relationship between x and y cannot be determined.
2) Answer: e)
I) 14x2 – 132x + 238 = 0
=> 2 x (7x2 – 66x + 119) = 0
=> 7x2 – 66x + 119 = 0
=> (x – 7)(7x – 17) = 0
=> x = 7, 17/7
II) 4y2 – 17y + 13 = 0
=> (y – 1)(4y – 13) = 0
=> y = 1, 13/4
Hence, relationship between x and y cannot be determined.
3) Answer: a)
I) 5x2 – 19x + 12 = 0
=> (5x – 4)(x – 3) = 0
=> x = 4/5, 3
II) 3y2 + 14y + 15 = 0
=> (y + 3)(3y + 5) = 0
=> y = -3, -5/3
Hence, x > y
4) Answer: e)
I) 4x2 + 3x – 10 = 0
=> (4x – 5)(x + 2) = 0
=> x = 5/4, -2
II) y2 – (343)1/3 – √841 = 0
=> y2 – 7 – 29 = 0
=> y2 = 36
=> y = ±6
Hence, relationship between x and y cannot be determined.
5) Answer: a)
I) 6x2 – 25x + 24 = 0
=> (2x – 3) (3x – 8) = 0
=> x = 3/2, 8/3
II) 5y2 + 27y + 10 = 0
=> (y + 5) (5y + 2) = 0
=> y = -5,
-2/5Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Hence, x > y
Directions (6-10) :
6) Answer: d)
From I:
Aman, Sunil and Kabir entered into a partnership for three years and at the end of three years they earned a profit of Rs.200000.
From II:
Ratio of investment amount of Aman, Sunil and Kabir is 3:5:4 respectively:.
From III:
At the end of two years, Kabir doubled his investment.
From I, II and III:
Let the investment amounts of Aman, Sunil and Kabir be Rs.3x, Rs.5x and Rs.4x respectively.
Ratio of share in the profit:
Aman : Sunil : Kabir = (3x + 3x + 3x) : (5x + 5x + 5x) : (4x + 4x + 8x)
= 9x: 15x: 16x
= 9:15:16
Share of Aman in the profit = 9/40 x 200000 = Rs.45000
Hence, all I, II and III together are sufficient.
7) Answer: d)
From I:
Speed(train) : Speed(bus) : Speed(car) = 8 : 2 : 3
From II:
Speed(car) = 216/8 = 27 km/h
From III:
Speed (bus) = 24/2 = 12 km/h
From I and II:
Speed (train) = 8/3 x 27 = 72 km/h
Required distance = 72 x 9 = 648 Km
From I and III:
Speed (train) = 8/2 x 12 = 48 km/h
Required distance = 48 x 9 = 432 km
Hence, only I and Either II or III are sufficient.
8) Answer: c)
From I:
Probability of drawing one red ball from the bag is 1/3
From II:
Red = 4
Green = 3
Blue = x (let)
From III:
Blue < Red
From I and II:
4/(4 + 3 + x) = 1/3
=> 12 = 4 + 3 + x
=> x = 12 – 7
=> x = 5
Required probability = 5/(4 + 3 + 5) = 5/12
Hence, only I and II are sufficient.
9) Answer: b)
From I and II:
Let the present ages of Mauli and Nandini be 5x years and 4x years respectively.
(5x – 5)/(4x – 5) = 4/3
=> 15x – 15 = 16x – 20
=> x = 5
Age of Mauli after ten years = 5x + 10 = 5 x 5 + 10 = 35 years
From I and III:
Let the present ages of Mauli and Nandini be 5x years and 4x years respectively.
(5x + 10)/(4x + 10) = 7/6
=> 30x + 60 = 28x + 70
=> 2x = 10
=> x = 5
Age of Mauli after ten years = 5x + 10 = 5 x 5 + 10 = 35 years
From II and III:
Let the ages of Mauli and Nandini before five years be 4x years and 3x years respectively
(4x + 15)/(3x + 15) = 7/6
=> 24x + 90 = 21x + 105
=> 3x = 15
=> x = 5
Age of Mauli after ten years = 4x + 15 = 4 x 5 + 15 = 35 years
Hence, any two of the three statements are sufficient.
10) Answer: d)
From I:
Roshni + Sitara + Kumud + Mini = 4 x 26 + 4 x 4 = 120 years
From II:
Roshni + Sitara = 2 x 31 = 62 years
From III:
Mini = Kumud – 2
From I, II and III
Roshni + Sitara + Kumud + Mini = 4 x 26 + 4 x 4 = 120 years
Roshni + Sitara = 2 x 31 = 62 years
Mini = Kumud – 2
Roshni + Sitara + Kumud + Mini = 120
=> 62 + kumud + Kumud – 2 = 120
=> 60 + 2 x kumud = 120
=> 2 x Kumud = 120 – 60
=> Kumud = 60/2
=> Kumud = 30 years
Hence, all I, II and III together are sufficient.
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