Quantitative Aptitude: Quadratic Equations Set 28

Quadratic Equations Practice Sets for IBPS PO, IBPS RRB, LIC, UIICL, OICL, Bank of Baroda and other competitive exams.

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. 4x² – 29x + 45 = 0,
   II. 4y² – 17y + 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

    Option C
   Solution: 
   4x² – 29x + 45 = 0
   4x² – 20x – 9x + 45 = 0
   Gives x = 9/4, 5
   4y² – 17y + 18 = 0
   4y² – 8y – 9y + 18 = 0
   Gives y = 2, 9/4
   
2. I. 3x² – 13x – 30 = 0,
   II. 2y² – 25y + 78 = 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 – 13x – 30 = 0
   3x² – 18x + 5x – 30 = 0
   Gives x = -5/3, 6
   2y² – 25y + 78 = 0
   2y² – 12y – 13y + 78 = 0
   Gives y = 6, 13/2
   
3. I. 3x² – 20x + 32 = 0,
   II. 3y² – 29y + 56 = 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 – 20x + 32 = 0
   3x² – 12x – 8x + 32 = 0
   Gives x = 8/3, 4
   3y² – 29y + 56 = 0
   3y² – 21y – 8y + 56 = 0
   Gives y = 8/3, 7
4. I. 3x² – 16x – 35 = 0,
   II. 3y² – 23y + 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 E
   Solution: 
   3x² – 16x – 35 = 0
   3x² – 21x + 5x – 35 = 0
   Gives x = -5/3, 7
   3y² – 23y + 40 = 0
   3y² – 15y – 8y+ 40 = 0
   Gives y= 8/3, 5
   
5. I. 2x² – 23x + 65 = 0,
   II. 3y² + 2y – 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

    Option A
   Solution: 
   2x² – 23x + 65 = 0
   2x² – 10x – 13x + 65 = 0
   Gives x = 5, 13/2
   3y² + 2y – 16 = 0
   3y² – 6y + 8y – 16 = 0
   Gives y= -8/3, 2
6. I. x² – 78 = 91,
   II. √3 y = √432
   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: 
   x² – 78 = 91
   x² = 169
   Gives x = -13, 13
   √3 y = √432
   y = √432/√3 = √144
   Gives y = 12
   Now when x = -13, y > x
   and when x = 13, y < x
   So relation cannot be established
   
7. I. 3x² + 17x + 10 = 0,
   II. 3y² + 14y – 5 = 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 + 17x + 10 = 0
   3x² + 15x + 2x + 10 = 0
   Gives x = -5, -2/3
   3y² + 14y – 5 = 0
   3y² + 15y – y – 5 = 0
   Gives y = -5, 1/3
   
8. I. 2x² – 13x + 15 = 0,
   II. 2y² + 5y – 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

    Option C
   Solution: 
   2x² – 13x + 15 = 0
   2x² – 10x – 3x + 15 = 0
   Gives x = 3/2, 5
   2y² + 5y – 12 = 0
   2y² + 8y -3y – 12 = 0
   Gives y= -4, 3/2
9. I. 2x² – 3x – 35 = 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 E
   Solution: 
   2x² – 3x – 35 = 0
   2x² – 10x + 7x – 35 = 0
   Gives x = -7/2, 5
   3y² + 11y + 6 = 0
   3y² + 9y +2y + 6 = 0
   Gives y= -3, -2/3
10. I. 3x² + 19x + 20 = 0,
    II. 3y² – 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

     Option B
    Solution: 
    3x² + 19x + 20 = 0
    3x² + 15x + 4x + 20 = 0
    Gives x = -5, -4/3
    3y² – 7y – 6 = 0
    3y² – 9y + 2y – 6 = 0
    Gives y= -2/3, 3

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