Quantitative Aptitude: Quadratic Equations 

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 + 27x + 18 = 0,
II. 2y² – 7y + 3 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

2.                     I. 3x² – 2x – 8 = 0,
II. 6y² – 17y + 10 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

3.                     I. 3² + 11x + 6 = 0,
II. 5y² + 16y + 3 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

4.                     I. 4x² – 11x + 6 = 0,
II. 6y² – 29y + 28 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

5.                     I. 3x² – 25x + 52 = 0,
II. 3y² – 8y – 16 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

6.                     I. 8x² + 10x + 3 = 0,
II. 3y² + 70y + 40 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

7.                     I. 50x² ¬¬– 95x + 42 = 0,
II. 50y² – 65y + 21 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined

8.                     I. 5x² – 13x + 6 = 0,
II. 3y² – 22y – 35 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

9.                     I. 3x² – 4x – 15 = 0,
II. 5y² – 11y – 18 = 0 
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

10.                 I. 2x² + 5x – 12 = 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

1.      Option B
Solution: 
4x² + 27x + 18 = 0
4x² + 24x + 3x + 18 = 0
So x = -3/4, -6
2y² – 7y + 3 = 0
2y² – 6y – y + 3 = 0
So y = 1/2, 3
Put all values on number line and analyze the relationship
-6… -3/4… 1/2… 3

2.      Option D
Solution: 
3x² – 2x – 8 = 0
3x² – 6x + 4x – 8 = 0
So x = -4/3, 2
6y² – 17y + 10 = 0
6y² – 12y – 5y + 10 = 0
So y = 5/6, 2
Put all values on number line and analyze the relationship
-4/3… 2… 5/6

3.      Option E
Solution: 
3² + 11x + 6 = 0
3² + 9x + 2x + 6 = 0
So x = -3, -2/3
5y² + 16y + 3 = 0
5y² + 15y + y + 3 = 0
So y = -1/5, -3
Put all values on number line and analyze the relationship
-3 …. -2/3 ….-1/5
Since the common value (-3) is not in between other 2 values, there is no relationship between x and y.

4.      Option E
Solution: 
4x² – 11x + 6 = 0
4x² – 8x – 3x + 6 = 0
So x = 3/4, 2
6y² – 29y + 28 = 0
6y² – 8y – 21y + 28 = 0
So y = 4/3, 7/2
Put all values on number line and analyze the relationship
3/4 …. 4/3….. 2…. 7/2

5.      Option C
Solution: 
3x² – 25x + 52 = 0
3x² – 12x – 13x + 52 = 0
So x = 4, 13/3
3y² – 8y – 16 = 0
3y² – 12y + 4y – 16 = 0
So y = 4, -4/3
Put all values on number line and analyze the relationship
-4/3 …. 4…. 13/3

6.      Option A
Solution: 
8x² + 10x + 3 = 0
8x² + 4x + 6x + 3 = 0
So x = -3/4, -1/2
3y² + 70y + 40 = 0
3y² + 30y + 40y + 40 = 0
So y = -10, -4/3
Put all values on number line and analyze the relationship
-10 … -4/3 …. -3/4 …. -1/2

7.      Option C
Solution: 
50x² ¬¬– 95x + 42 = 0
50x² ¬¬– 60x – 35x + 42 = 0
So x = 7/10, 6/5
50y² – 65y + 21 = 0
50y² – 65y + 21 = 0
So y = 3/5, 7/10
Put all values on number line and analyze the relationship
3/5…. 7/10…. 6/5

8.      Option B
Solution: 
5x² – 13x + 6 = 0
5x² – 10x – 3x + 6 = 0
So x = 3/5, 2
3y² – 22y – 35 = 0
3y² – 15y – 7y – 35 = 0
So y = 7/3, 5
Put all values on number line and analyze the relationship
3/5…. 2…. 7/3… 5

9.      Option E
Solution: 
3x² – 4x – 15 = 0
3x² – 9x + 5x – 15 = 0
So x = -5/3, 3
5y² – 11y – 18 = 0
5y² – 15y + 6y – 18 = 0
So y = -6/5, 3
Put all values on number line and analyze the relationship
-5/3….. -6/5…. 3
Since the common value (3) is not in between other 2 values, there is no relationship between x and y.

10. Option B
Solution: 
2x² + 5x ¬– 12 = 0
2x² + 8x ¬– 3x – 12 = 0
So x = -4 , 3/2
2y² – 19y + 35 = 0
2y² – 14y – 5y + 35 = 0
So y = 5/2, 7
Put all values on number line and analyze the relationship
-4……. 3/2…… 5/2…