Quantitative Aptitude: Quadratic Equations Set 10

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. 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
3. 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
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. 6x² + 5x – 1 = 0,
   II. 3y² – 11y + 6 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   View Answer

   Option B
   Solution:
   6x² + 5x – 1 = 0
   6x² + 6x – x – 1 = 0
   Gives x = -1, 1/6
   3y² – 11y + 6 = 0
   3y² – 9y – 2y + 6 = 0
   Gives y = 2/3, 3
   Put on number line
   -1… 1/6… 2/3… 3
   
6. I. 3x² + 4x – 4 = 0,
   II. 4y² + 5y – 6 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   View Answer

   Option E
   Solution:
   3x² + 4x – 4 = 0
   3x² + 6x – 2x – 4 = 0
   Gives x = -2, 2/3
   4y² + 5y – 6 = 0
   4y² + 5y – 6 = 0
   Gives y = -2, 3/4
   Put on number line
   -2…. 2/3… 3/4
   When x=2/3, x>y(= -2) and x<y(= 3/4)
   So cant be determined
   
7. I. 5x² – 36x – 32 = 0,
   II. 3y² – 17y – 6 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If 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
   Put on number line
   -4/5…. -1/3… 6… 8
   
8. I. 3x² – 25x + 52 = 0,
   II. 15y² – 38y – 40 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   View Answer

   Option A
   Solution:
   3x² – 25x + 52 = 0
   3x² – 12x – 13x + 52 = 0
   Gives x = 4, 13/3
   15y² – 38y – 40 = 0
   15y² + 12y – 50y – 40 = 0
   Gives y = -4/5, 10/3
   Put on number line
   -4/5… 10/3… 4… 13/3
   
9. I. 6x² + x – 2 = 0,
   II. 2y² + 11y + 14 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   View Answer

   Option A
   Solution:
   6x² + x – 2 = 0
   6x² + 4x – 3x – 2 = 0
   Gives x = -2/3, 1/2
   2y² + 11y + 14 = 0
   2y² + 4y + 7y + 14 = 0
   Gives y = -7/2, -2
   
10. I. 3x² + 14x – 5 = 0,
    II. 3y² – 19y + 6 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If X = Y or relation cannot be established
    
    View Answer

    Option D
    Solution:
    3x² + 14x – 5 = 0
    3x² + 15x – x – 5 = 0
    Gives x = -5, 1/3
    3y² – 19y + 6 = 0
    3y² – 18y – y + 6 = 0
    Gives y = 1/3, 6
    Put on number line
    -5…. 1/3… 6