Quantitative Aptitude: Quadratic Equations Set 7

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 – 17x + 10 = 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 C
   Solution:
   3x² – 17x + 10 = 0
   3x² – 15x – 2x + 10 = 0
   Gives x = 2/3, 5
   3y² + 4y – 4 = 0
   3y² + 6y – 2y – 4 = 0
   Gives y = -2, 2/3
   Put all values on number line and analyze the relationship
   -2…. 2/3…… 5
2. I. 3x² – 14x + 8 = 0
   II. 3y² – 20y + 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 – 14x +8 = 0
   3x² – 12x – 2x + 8 = 0
   Gives x = 2/3, 4
   3y² – 20y + 12 = 0
   3y² – 18y – 2y + 12 = 0
   Gives y = 6, 2/3
   Put all values on number line and analyze the relationship
   2/3….. 4….. 6
3. I. 3x² – 19x + 28 = 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 A
   Solution:
   4x² – 19x + 28 = 0
   4x² – 12x – 7x + 28 = 0
   Gives x = 7/3, 4
   4y² – 5y – 6 = 0
   4y² – 8y + 3y – 6 = 0
   Gives y = -3/4, 2
   Put all values on number line and analyze the relationship
   -3/4…… 2…… 7/3…. 4
4. I. 6x² + 23x + 21 = 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:
   6x² + 23x + 21 = 0
   6x² + 9x + 14x + 21 = 0
   Gives x = -7/3, -3/2
   3y² – 14y – 5 = 0
   3y² – 15y + y – 5 = 0
   Gives y = -1/3, 5
   Put all values on number line and analyze the relationship
   -7/3…… -3/2….. -1/3…… 5
5. I. 2x² – 7x + 3 = 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 A
   Solution:
   2x² – 7x + 3 = 0
   2x² – 6x – x + 3 = 0
   Gives x = 3, 1/2
   2y² + 11y + 12 = 0
   2y² + 8y + 3y + 12 = 0
   Gives y = -3/2, -4
   Put all values on number line and analyze the relationship
   -4……. -3/2…… 1/2….. 3
6. I. 3x² + 22x + 35 = 0
   II. 6y² + 11y – 7 = 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:
   3x² + 22x + 35 = 0
   3x² + 15x + 7x + 35 = 0
   Gives x = -5, -7/3
   6y² + 11y – 7 = 0
   6y² – 3y + 14y – 7 = 0
   Gives y = 1/2, -7/3
   Put all values on number line and analyze the relationship
   -5….. -7/3….. 1/2
7. I. 2x² – 3x – 9 = 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:
   2x² – 3x – 9 = 0
   2x² – 6x + 3x – 9 = 0
   Gives x = -3/2, 3
   3y² + 11y + 6 = 0
   3y² + 9y + 2y + 6 = 0
   Gives y = -3, -2/3
   Put all values on number line and analyze the relationship
   -3….. -3/2….. -2/3…. 3
8. I. x² + 14x + 45 = 0
   II. 3y² – y – 10 = 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:
   x² + 14x + 45 = 0
   x² + 9x + 5x + 45 = 0
   Gives x = -9, -5
   3y² – y – 10 = 0
   3y² – 6y + 5y – 10 = 0
   Gives y = -5/3, 2
   Put all values on number line and analyze the relationship
   -9…….. -5….. -5/3……. 2
9. I. 4x² + 17x + 15 = 0
   II. 4y² – 3y – 10 = 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 + 17x + 15 = 0
   4x² + 12x + 5x + 15 = 0
   Gives x = -3, -5/4
   4y² – 3y – 10 = 0
   4y² – 8y + 5y – 10 = 0
   Gives y = -5/4, 2
   Put all values on number line and analyze the relationship
   -3…… -5/4…… 2
10. I. 2x² – 17x + 36 = 0
    II. 3y² – 14y + 8 = 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 – 17x + 36 = 0
    2x² – 8x – 9x + 36 = 0
    Gives x = 4, 9/2
    3y² – 14y + 8 = 0
    3y² – 12y + 2y + 8 = 0
    Gives y = 2/3, 4
    Put all values on number line and analyze the relationship
    2/3…… 4…… 9/2