Quantitative Aptitude: Quadratic Equations Set 11

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. 3x² – 8x + 4 = 0
   II. 3y² – 16y + 16 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option E
   Solution:
   3x² – 8x + 4 = 0
   3x² – 2x – 6x + 4 = 0
   Gives x = 2, 2/3
   3y² – 16y + 16 = 0
   3y² – 12y – 4y + 16 = 0
   Gives y = 4, 4/3
   
2. I. 3x² + 10x + 7 = 0
   II. 2y² – 5y – 12 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option E
   Solution:
   3x² + 10x + 7 = 0
   3x² + 3x + 7x + 7 = 0
   Gives x = -1, -7/3
   2y² – 5y – 12 = 0
   2y² – 8y + 3y – 12 = 0
   Gives y = -3/2, 4
   
3. I. 4x² + 15x + 9 = 0
   II. 4y² – 13y – 12 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option D
   Solution:
   4x² + 15x + 9 = 0
   4x² + 12x + 3x + 9 = 0
   Gives x = -3, -3/4
   4y² – 13y – 12 = 0
   4y² – 16y + 3y – 12 = 0
   Gives y = -3/4, 4
   
4. I. 3x² + 23x + 30 = 0
   II. 3y² – 4y – 4 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option B
   Solution:
   3x² + 23x + 30 = 0
   3x² + 18x + 5x + 30 = 0
   Gives x = -5/3, -6
   3y² – 4y – 4 = 0
   3y² – 6y + 2y – 4 = 0
   Gives y = 2, -2/3
   Put all values on number line and analyze the relationship
   -6…. -5/3….. -2/3…… 2
5. I. 5x² – 36x – 32 = 0,
   II. 3y² – 11y + 6 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option E
   Solution:
   5x² – 36x – 32 = 0
   5x² + 4x – 40x – 32 = 0
   Gives x = -4/5, 8
   3y² – 17y – 6 = 0
   3y² + y – 18y – 6 = 0
   Gives y = -1/3, 6
   
6. I. 4x² + 17x + 18 = 0,
   II. 3y² + 4y – 4 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option D
   
7. I. 4x² – 9x – 9 = 0,
   II. 4y² + 11y + 6 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option C
   
8. I. 3x² – 19x + 28 = 0,
   II. 4y² – 11y + 6 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option A
   
9. I. 3x² + 19x + 28 = 0,
   II. 6y² – y – 2 = 0A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relation cannot be established
   
   View Answer

   Option B
   
   
10. I. 3x² + 7x – 6 = 0,
    II. 6y² – y – 2 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    
    View Answer

    Option E
    Solution:
    3x² + 7x – 6 = 0
    3x² + 9x – 2x – 6 = 0
    Gives x = -3, 2/3
    6y² – y – 2 = 0
    6y² + 3y – 4y – 2 = 0
    Gives y = -1/2, 2/3