# Quantitative Aptitude: Quadratic Equations Set 10

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 + 22 x + 24 = 0
II. 2y2 + 11y + 12 = 0
A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relation cannot be established
Option E
Solution:

3x2 + 22 x + 24 = 0
3x2 + 18x + 4x + 24 = 0
Gives x = -4/3, -6
2y2 + 11y + 12 = 0
2y2 + 8y + 3y + 12 = 0
Gives y = -4, -3/2
Put all values on number line and analyze the relationship
-6â€¦..-4â€¦. -3/2â€¦.-4/3
2. I. 3x2 + 7x â€“ 6 = 0
II. 6y2 – 35y + 50 = 0
A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relation cannot be established
Option B
Solution:

3x2 + 7x â€“ 6 = 0
3x2 + 9x â€“ 2x â€“ 6 = 0
Gives x = -3, 2/3
6y2 – 35y + 50 = 0
6y2 – 15y â€“ 20y + 50 = 0
Gives y = 5/2, 10/3
Put all values on number line and analyze the relationship
-3â€¦ 2/3â€¦ 5/2â€¦. 10/3
3. I. 4x2 + 13x + 10 = 0
II. 4y2 – 7y â€“ 15 = 0
A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relation cannot be established
Option D
Solution:

4x2 + 13x + 10 = 0
4x2 + 8x + 5x + 10 = 0
Gives x = -2, -5/4
4y2 – 7y â€“ 15 = 0
4y2 – 12y + 5y â€“ 15 = 0
Gives y = -5/4, 3
Put all values on number line and analyze the relationship
-2â€¦ -5/4â€¦. 3
4. I. 3x2 + 23x + 30 = 0
II. 3y2 â€“ 4y â€“ 4 = 0
A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relation cannot be established
Option B
Solution:

3x2 + 23x + 30 = 0
3x2 + 18x + 5x + 30 = 0
Gives x = -5/3, -6
3y2 – 4y – 4 = 0
3y2 – 6y + 2y – 4 = 0
Gives y = 2, -2/3
Put all values on number line and analyze the relationship
-6â€¦. -5/3â€¦.. -2/3â€¦â€¦ 2
5. I. 6x2 + 5x â€“ 1 = 0,
II. 3y2 â€“ 11y + 6 = 0
A) If X > Y
B) If X < Y
C) If X â‰¥ Y
D) If X â‰¤ Y
E) If X = Y or relation cannot be established
Option B
Solution:

6x2 + 5x â€“ 1 = 0
6x2 + 6x â€“ x â€“ 1 = 0
Gives x = -1, 1/6
3y2 â€“ 11y + 6 = 0
3y2 â€“ 9y â€“ 2y + 6 = 0
Gives y = 2/3, 3
Put on number line
-1… 1/6â€¦ 2/3â€¦ 3
6. I. 3x2 + 4x â€“ 4 = 0,
II. 4y2 + 5y â€“ 6 = 0
A) If X > Y
B) If X < Y
C) If X â‰¥ Y
D) If X â‰¤ Y
E) If X = Y or relation cannot be established
Option E
Solution:

3x2 + 4x â€“ 4 = 0
3x2 + 6x â€“ 2x â€“ 4 = 0
Gives x = -2, 2/3
4y2 + 5y â€“ 6 = 0
4y2 + 5y â€“ 6 = 0
Gives y = -2, 3/4
Put on number line
-2â€¦. 2/3â€¦ 3/4
When x=2/3, x>y(= -2) and x<y(= 3/4)
So cant be determined
7. I. 5x2 â€“ 36x â€“ 32 = 0,
II. 3y2 â€“ 17y â€“ 6 = 0
A) If X > Y
B) If X < Y
C) If X â‰¥ Y
D) If X â‰¤ Y
E) If X = Y or relation cannot be established
Option E
Solution:

5x2 – 36x â€“ 32 = 0
5x2 + 4x – 40x â€“ 32 = 0
Gives x = -4/5, 8
3y2 â€“ 17y â€“ 6 = 0
3y2 + y â€“ 18y â€“ 6 = 0
Gives y= -1/3, 6
Put on number line
-4/5â€¦. -1/3â€¦ 6â€¦ 8
8. I. 3x2 â€“ 25x + 52 = 0,
II. 15y2 â€“ 38y â€“ 40 = 0
A) If X > Y
B) If X < Y
C) If X â‰¥ Y
D) If X â‰¤ Y
E) If X = Y or relation cannot be established
Option A
Solution:

3x2 – 25x + 52 = 0
3x2 – 12x â€“ 13x + 52 = 0
Gives x = 4, 13/3
15y2 â€“ 38y – 40 = 0
15y2 + 12y â€“ 50y – 40 = 0
Gives y = -4/5, 10/3
Put on number line
-4/5… 10/3â€¦ 4â€¦ 13/3
9. I. 6x2 + x – 2 = 0,
II. 2y2 + 11y + 14 = 0
A) If X > Y
B) If X < Y
C) If X â‰¥ Y
D) If X â‰¤ Y
E) If X = Y or relation cannot be established
Option A
Solution:

6x2 + x – 2 = 0
6x2 + 4x â€“ 3x – 2 = 0
Gives x = -2/3, 1/2
2y2 + 11y + 14 = 0
2y2 + 4y + 7y + 14 = 0
Gives y = -7/2, -2
10. I. 3x2 + 14x â€“ 5 = 0,
II. 3y2 â€“ 19y + 6 = 0
A) If X > Y
B) If X < Y
C) If X â‰¥ Y
D) If X â‰¤ Y
E) If X = Y or relation cannot be established
Option D
Solution:

3x2 + 14x â€“ 5 = 0
3x2 + 15x â€“ x â€“ 5 = 0
Gives x = -5, 1/3
3y2 â€“ 19y + 6 = 0
3y2 â€“ 18y â€“ y + 6 = 0
Gives y = 1/3, 6
Put on number line
-5â€¦. 1/3â€¦ 6

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