Quantitative Aptitude: Quadratic Equations Set 5

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 + 22 x + 24 = 0
   II. 2y² + 11y + 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 + 22 x + 24 = 0
   3x² + 18x + 4x + 24 = 0
   Gives x = -4/3, -6
   2y² + 11y + 12 = 0
   2y² + 8y + 3y + 12 = 0
   Gives y = -4, -3/2
   Put all values on number line and analyze the relationship
   -6…..-4…. -3/2….-4/3
2. I. 20x² – 31x + 12 = 0
   II. 4y² + 5y – 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
   Solution:
   20x² – 31x + 12 = 0
   20x² – 16x – 15x + 12 = 0
   Gives x = 3/4, 4/5
   4y² + 5y – 6 = 0
   4y² + 5y – 6 = 0
   Gives y = -2, 3/4
   Put all values on number line and analyze the relationship
   -2…. 3/4… 4/5
3. I. 3x² + 14x – 5 = 0
   II. 4y² + 5y – 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:
   3x² + 14x – 5 = 0
   3x² + 15x – x – 5 = 0
   Gives x = -5, 1/3
   4y² + 5y – 6 = 0
   4y² + 5y – 6 = 0
   Gives y = -2, 3/4
   Put all values on number line and analyze the relationship
   -5….-2….. 1/3…. 3/4
4. I. 2x² – 15x + 7 = 0
   II. 8y² + 6y – 5 = 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
   Solution:
   2x² – 15x + 7 = 0
   2x² – 14x – x + 7 = 0
   Gives x = 1/2, 7
   8y² + 6y – 5 = 0
   8y² – 4y + 10y – 5 = 0
   Gives y = -5/4, 1/2
   Put all values on number line and analyze the relationship
   -5/4…. 1/2 …. 7
5. I. 3x² + 16x + 20 = 0
   II. 3y² – 14y – 5 = 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 + 16x + 20 = 0
   3x² + 6x + 10x + 20 = 0
   Gives x = -2, -10/3
   3y² – 14y – 5 = 0
   3y² – 15y + y – 5 = 0
   Gives y = -1/3, 5
   Put all values on number line and analyze the relationship
   -10/3… -2…. -1/3…. 5
6. I. 3x² + 7x – 6 = 0
   II. 6y² – 35y + 50 = 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 + 7x – 6 = 0
   3x² + 9x – 2x – 6 = 0
   Gives x = -3, 2/3
   6y² – 35y + 50 = 0
   6y² – 15y – 20y + 50 = 0
   Gives y = 5/2, 10/3
   Put all values on number line and analyze the relationship
   -3… 2/3… 5/2…. 10/3
7. I. 7x² – 11x – 6 = 0
   II. 6y² + 13y + 5 = 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
   Solution:
   7x² – 11x – 6 = 0
   7x² – 14x + 3x – 6 = 0
   Gives x = -3/7, 2
   6y² + 13y + 5 = 0
   6y² + 3y + 10y + 5 = 0
   Gives y = -5/3, -1/2
   Put all values on number line and analyze the relationship
   -5/3…. -1/2…. -3/7….. 2
8. I. 3x² + 4x – 39 = 0
   II. 3y² – 5y – 78 = 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 + 4x – 39 = 0
   3x² – 9x + 13x – 39 = 0
   Gives x = -13/3, 3
   3y² – 5y – 78 = 0
   3y² – 18y + 13y – 78 = 0
   Gives y = -13/3, 6
   Put all values on number line and analyze the relationship
   -13/3…. 3…. 6
9. I. 4x² + 13x + 9 = 0
   II. 3y² – 7y – 20 = 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:
   4x² + 13x + 9 = 0
   4x² + 4x + 9x + 9 = 0
   Gives x = -9/4, -1
   3y² – 7y – 20 = 0
   3y² – 12y + 5y – 20 = 0
   Gives y = -5/3, 4
   Put all values on number line and analyze the relationship
   -9/4…. -5/3…. -1….4
10. I. 4x² + 13x + 10 = 0
    II. 4y² – 7y – 15 = 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 + 13x + 10 = 0
    4x² + 8x + 5x + 10 = 0
    Gives x = -2, -5/4
    4y² – 7y – 15 = 0
    4y² – 12y + 5y – 15 = 0
    Gives y = -5/4, 3
    Put all values on number line and analyze the relationship
    -2… -5/4…. 3