Quantitative Aptitude: Quadratic Equations Set 16

Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-

1. I. 4x2 + 5x â€“ 6 = 0,
II. 2y2 + 11y + 12 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option E
Solution:

4x2 + 5x â€“ 6 = 0
4x2 + 8x â€“ 3x â€“ 6 = 0
Gives x = -2, 3/4
2y2 + 11y + 12 = 0
2y2 + 8y + 3y + 12 = 0
Gives y = -4, -3/2
2. I. 12x2 – 49x + 30 = 0,
II. 6y2 – 35y + 50 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option E
Solution:

12x2 – 49x + 30 = 0
12x2 – 9x â€“ 40x + 30 = 0
Gives x = 3/4, 10/3
6y2 – 35y + 50 = 0
6y2 – 15y â€“ 20y + 50 = 0
Gives y = 5/2, 10/3
3. I. 4x2 + 13x + 10 = 0,
II. 4y2 â€“ 7y – 15 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option D
Solution:

4x2 + 13x + 10 = 0
4x2 + 8x + 5x + 10 = 0
Gives x = -2, -5/4
4y2 â€“ 7y – 15 = 0
4y2 – 12y + 5y – 15 = 0
Gives y = -5/4, 3
4. I. 12x2 â€“ 5x â€“ 3 = 0,
II. 6y2 + y – 2 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option E
Solution:

12x2 â€“ 5x â€“ 3 = 0
12x2 + 4x â€“ 9x â€“ 3 = 0
Gives x = -1/3, 3/4
6y2 + y – 2 = 0
6y2 – 3y + 4y – 2 = 0
Gives y= -2/3, 1/2
5. I. 3x2 + 7x â€“ 6 = 0,
II. 3y2 â€“ 11y + 6 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option D
Solution:

Explanation:
3x2 + 7x â€“ 6 = 0
3x2 + 9x â€“ 2x â€“ 6 = 0
Gives x = -3, 2/3
3y2 â€“ 11y + 6 = 0
3y2 â€“ 9y â€“ 2y + 6 = 0
Gives y = 2/3, 3
6. I. 5x2 â€“ 36x â€“ 32 = 0,
II. 3y2 + 16y + 20 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option A
Solution:

5x2 – 36x â€“ 32 = 0
5x2 + 4x – 40x â€“ 32 = 0
Gives x = -4/5, 8
3y2 + 16y + 20 = 0
3y2 + 6y + 10y + 20 = 0
Gives y = -10/3, -2
7. I. 3x2 – (6 + 2âˆš3)x + 4âˆš3 = 0,
II. 3y2 – (2 + 3âˆš3)y + 2âˆš3 = 0
A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relationship cannot be determined
Option E
Solution:

3x2 – (6 + 2âˆš3)x + 4âˆš3 = 0
(3x2 – 6x) â€“ (2âˆš3x – 4âˆš3) = 0
3x (x- 2) – 2âˆš3 (x â€“ 2) = 0,
So x = 2, 2âˆš3/3 (1.15)
3y2 – (2 + 3âˆš3)y + 2âˆš3 = 0
(3y2 – 2y) – (3âˆš3y – 2âˆš3) = 0
y (3y â€“ 2) – âˆš3 (3y â€“ 2) = 0
So x = 2/3, âˆš3 (1.73)
8. I. 2x2 + (4 + âˆš2)x + 2âˆš2 = 0
II. y2 – (1 + 3âˆš3)y + 3âˆš3 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option B
Solution:

2x2 + (4 + âˆš2)x + 2âˆš2 = 0
(2x2 + 4x) + (âˆš2x + 2âˆš2) = 0
2x (x + 2) + âˆš2 (x + 2) = 0
So x = -2, -âˆš2/2 (-0.7)
y2 – (1 + 3âˆš3)y + 3âˆš3 = 0
(y2 – y) – (3âˆš3y – 3âˆš3) = 0
y (y â€“ 1) – 3âˆš3 (y â€“ 1) = 0
So, y = 1, 3âˆš3 (5.2)
9. I. x2 + (3 + 2âˆš2)x + 6âˆš2 = 0
II. 5y2 – (1 + 5âˆš2)y + âˆš2 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option B
Solution:

x2 + (3 + 2âˆš2)x + 6âˆš2 = 0
(x2 + 3x) + (2âˆš2x + 6âˆš2) = 0
x (x + 3) + 2âˆš2 (x + 3) = 0
So x = -3, -2âˆš2
5y2 – (1 + 5âˆš2)y + âˆš2 = 0
(5y2 – y) – (5âˆš2y – âˆš2) = 0
y (5y â€“ 1) – 3âˆš2 (5y â€“ 1) = 0
So, y = 1/5, 3âˆš2
10. I. 2x2 + (4 + 2âˆš6)x + 4âˆš6 = 0
II. 5y2 + (10 + âˆš6)y + 2âˆš6 = 0
A) If x > y
B) If x < y
C) If x â‰¥ y
D) If x â‰¤ y
E) If x = y or relation cannot be established
Option D
Solution:

2x2 + (4 + 2âˆš6)x + 4âˆš6 = 0
(2x2 + 4x) + (2âˆš6x + 4âˆš6) = 0
2x (x + 2) + 2âˆš6 (x + 2) = 0
So x = -2, -âˆš6
5y2 + (10 + âˆš6)y + 2âˆš6 = 0
(5y2 + 10y) + (âˆš6y + 2âˆš6) = 0
5y (y + 2) + âˆš6 (y + 2) = 0
So, y = -2, -âˆš6/5

38 Thoughts to “Quantitative Aptitude: Quadratic Equations Set 16”

1. Shilpa Thakur

q 1 ????????// kya answer hi hoga?????????// -2 is < -1.5 so e nhi hoga kya

1. Yes its E
Alternate roots

1. Shilpa Thakur

okk////////// thank you

2. Divaker

some questions are confusing but solvable thx

3. Sunil Sharma

question 10 . answer should be D part. x<=y

4. sachin shukla@ my turn 2017

ty)))

5. Deepak sahu

Mam 10nth question me E Option hoga plz chech kariye

1. D hi hai

Root 6 is -2.4
-2 will come in middle

6. MiMi

thnk u mam :)))

7. jaga

thank u mam

8. Ayushi

thanku

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