Quantitative Aptitude: Quadratic Equations Set 1

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. 20x² – 31x + 12 = 0,
   II. 6y² – 7y + 2 = 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

   A) If x > y
   Solution:
   20x² – 31x + 12 = 0
   20x² – 16x – 15x + 12 = 0
   So x = 3/4, 4/5
   6y² – 7y + 2 = 0
   6y² – 3y – 4y + 2 = 0
   So y = 1/2, 2/3
   Put on number line
   1/2… 2/3… 3/4… 4/5
2. I. 3x² + 22 x + 24 = 0,
   II. 3y² – 10y + 3 = 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

   B) If x < y
   Solution:
   3x² + 22 x + 24 = 0
   3x² + 18x + 4x + 24 = 0
   So x = -4/3, -6
   3y² – 10y + 3 = 0
   3y² – 9y – y + 3 = 0
   So y = 1/3, 3
   Put on number line
   -6… -4/3… 1/3… 3
3. I. 6x² – x – 2 = 0,
   II. 5y² – 18y + 9 = 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

   E) If x = y or relation cannot be established
   Solution:
   6x² – x – 2 = 0
   6x² + 3x – 4x – 2 = 0
   So x = -1/2, 2/3
   5y² – 18y + 9 = 0
   5y² – 15y – 3y + 9 = 0
   So y = 3/5, 3
   Put on number line
   -1/2 …. 3/5 ….2/3 …. 3
   
4. I. x² – x – 6 = 0,
   II. 5y² – 7y – 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

   E) If x = y or relation cannot be established
   Solution:
   x² – x – 6 = 0
   x² – 2x + 3x – 6 = 0
   So x = -3, 2
   5y² – 7y – 6 = 0
   5y² – 10y + 3y – 6 = 0
   So y = -3/5, 2
   Put on number line
   -3 …. -3/5….. 2
5. I. 3x² – 10x + 8 = 0,
   II. 3y² + 8y – 16 = 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

   C) If x ≥ y
   Solution:
   3x² – 10x + 8 = 0
   3x² – 6x – 4x + 8 = 0
   So x = 2, 4/3
   3y² + 8y – 16 = 0
   3y² + 12y – 4y – 16 = 0
   So y = -4, 4/3
   Put on number line
   -4 …. 4/3…. 2
6. I. 2x² + 17x + 30 = 0,
   II. 2y² + 13y + 18 = 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

   E) If x = y or cannot be established
   Solution:
   2x² + 17x + 30 = 0
   2x² + 12x + 5x + 30 = 0
   So x = -6, -5/2
   2y² + 13y + 18 = 0
   2y² + 4y + 9y + 18 = 0
   So y = -9/2, -2
   Put on number line
   -6 … -9/2 …. -5/2 …. -2
   
7. I. 3x² + 16x + 20 = 0,
   II. 3y² + 8y + 4 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relationship cannot be determined
   
   View Answer

   D) If x ≤ y
   Solution:
   3x² + 16x + 20 = 0
   3x² + 6x + 10x + 20 = 0
   So x = -10/3, -2
   3y² + 8y + 4 = 0
   3y² + 6y + 2y + 4 = 0
   So y = -2, -2/3
   put on number line
   -10/3…. -2…. -2/3
8. I. x² + x – 20 = 0,
   II. 2y² + 13y + 15 = 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

   E) If x = y or relation cannot be established
   Solution:
   x² + x – 20 = 0
   (x+5)(x-4) = 0
   So x = -5, 4
   2y² + 13y + 15 = 0
   2y² + 10y + 3y + 15 = 0
   So y = -5, -3/2
   Put on number line
   -5…. -3/2…. 4
9. I. 5x² – 7x – 6 = 0,
   II. 5y² + 23y + 12 = 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

   C) If x ≥ y
   Solution:
   5x² – 7x – 6 = 0
   5x² – 10x + 3x – 6 = 0
   So x = -3/5, 2
   5y² + 23y + 12 = 0
   5y² + 20y + 3y + 12 = 0
   So y = -4, -3/5
   Put on number line
   -4….. -3/5…. 2
10. I. 2x² – 9x + 4 = 0,
    II. 2y² + 7y – 4 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    
    View Answer

    C) If x ≥ y
    Solution:
    2x² – 9x + 4 = 0
    2x² – 8x – x + 4 = 0
    So x = 4 , 1/2
    2y² + 7y – 4 = 0
    2y² + 8y – y – 4 = 0
    So y = -4, 1/2
    Put on number line
    -4……. 1/2…… 4