Quantitative Aptitude: Quadratic Equations Set 3

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 + 20x + 32 = 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 + 20x + 32 = 0
   3x² + 12x + 8x + 32 = 0
   So x = -4, -8/3
   3y² – 4y – 4 = 0
   3y² – 6y + 2y – 4 = 0
   So y = -2/3, 2
   Put all values on number line and analyze the relationship
   -4… -8/3… -2/3… 2
2. I. 4x² – 12x + 5 = 0,
   II. 6y² – 13y + 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:
   4x² – 12x + 5 = 0
   4x² – 2x – 10x + 5 = 0
   So x = ½, 5/2
   6y² – 13y + 6 = 0
   6y² – 4y – 9y + 6 = 0
   So y = 2/3, 3/2
   Put all values on number line and analyze the relationship
   1/2… 2/3… 3/2…. 5/2
3. I. 3² – 14x + 16 = 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:
   3² – 14x + 16 = 0
   3² – 6x – 8x + 16 = 0
   So x = 8/3, 2
   4y² – 5y – 6 = 0
   4y² – 8y + 3y – 6 = 0
   So y = -3/4, 2
   Put all values on number line and analyze the relationship
   -3/4 …. 2 ….8/3
   
4. I. 5x² – 8x – 4 = 0,
   II. 5y² – 23y – 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 E
   Solution:
   5x² – 8x – 4 = 0
   5x² – 10x + 2x – 4 = 0
   So x = -2/5, 2
   5y² – 23y – 10 = 0
   5y² – 25y + 2y – 10 = 0
   So y = -2/5, 5
   Put all values on number line and analyze the relationship
   -2/5 …. 2….. 5
5. I. 3x² + 13x + 14 = 0,
   II. 4y² + 9y + 2 = 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 + 13x + 14 = 0
   3x² + 6x + 7x + 14 = 0
   So x = -7/3, -2
   4y² + 9y + 2 = 0
   4y² + 8y + y + 2 = 0
   So y = -2, -1/4
   Put all values on number line and analyze the relationship
   -7/3 …. -2…. -1/4
6. I. 3x² + 8x + 5 = 0,
   II. 5y² – 7y – 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 B
   Solution:
   3x² + 8x + 5 = 0
   3x² + 3x + 5x + 5 = 0
   So x = -5/3, -1
   5y² – 7y – 6 = 0
   5y² – 7y – 6 = 0
   So y = -3/5, 2
   Put all values on number line and analyze the relationship
   -5/3…. -1…. -3/5…. 2
   
7. I. 3x² ¬¬+ 16x + 20 = 0,
   II. 3y² + 14y + 16 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relationship cannot be determined
   
   View Answer

   Option E
   Solution:
   3x² ¬¬+ 16x + 20 = 0
   3x² ¬¬+ 6x + 10x + 20 = 0
   So x = -10/3, -2
   3y² + 14y + 16 = 0
   3y² + 6y + 8y + 16 = 0
   So y = -8/3, -2
   Put all values on number line and analyze the relationship
   -10/3…. -8/3…. -2
8. I. 4x² – 9x + 2 = 0,
   II. 3y² – 16y + 21 = 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:
   4x² – 9x + 2 = 0
   4x² – 8x – x + 2 = 0
   So x = 1/4, 2
   3y² – 16y + 21 = 0
   3y² – 9y – 7y + 21 = 0
   So y = 7/3, 3
   Put all values on number line and analyze the relationship
   1/4…. 2…. 7/3… 3
9. I. 3x² + 5x + 2 = 0,
   II. 3y² + 11y + 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 A
   Solution:
   3x² + 5x + 2 = 0
   3x² + 3x + 2x + 2 = 0
   So x = -1, -2/3
   3y² + 11y + 10 = 0
   3y² + 6y + 5y + 10 = 0
   So y = -2, -5/3
   Put all values on number line and analyze the relationship
   -2….. -5/3…. -1….. -2/3
   
10. I. 4x² – 9x + 2 = 0,
    II. 2y² – 19y + 35 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    
    View Answer

    Option B
    Solution:
    4x² – 9x + 2 = 0
    4x² – 8x – x + 2 = 0
    So x = 1/4, 2
    2y² – 19y + 35 = 0
    2y² – 14y – 5y + 35 = 0
    So y = 5/2, 7
    Put all values on number line and analyze the relationship
    1/4……. 2…… 5/2…7