# Quantitative Aptitude: Quadratic Equations Set 1

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. 20x2 â€“ 31x + 12 = 0,
II. 6y2 â€“ 7y + 2 = 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
A) If x > y
Solution:

20x2 â€“ 31x + 12 = 0
20x2 â€“ 16x â€“ 15x + 12 = 0
So x = 3/4, 4/5
6y2 â€“ 7y + 2 = 0
6y2 â€“ 3y â€“ 4y + 2 = 0
So y = 1/2, 2/3
Put on number line
1/2â€¦ 2/3â€¦ 3/4â€¦ 4/5
2. I. 3x2 + 22 x + 24 = 0,
II. 3y2 â€“ 10y + 3 = 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
B) If x < y
Solution:

3x2 + 22 x + 24 = 0
3x2 + 18x + 4x + 24 = 0
So x = -4/3, -6
3y2 â€“ 10y + 3 = 0
3y2 â€“ 9y â€“ y + 3 = 0
So y = 1/3, 3
Put on number line
-6… -4/3â€¦ 1/3â€¦ 3
3. I. 6x2 â€“ x â€“ 2 = 0,
II. 5y2 â€“ 18y + 9 = 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
E) If x = y or relation cannot be established
Solution:

6x2 â€“ x â€“ 2 = 0
6x2 + 3x â€“ 4x â€“ 2 = 0
So x = -1/2, 2/3
5y2 â€“ 18y + 9 = 0
5y2 â€“ 15y â€“ 3y + 9 = 0
So y = 3/5, 3
Put on number line
-1/2 â€¦. 3/5 â€¦.2/3 â€¦. 3
4. I. x2 â€“ x â€“ 6 = 0,
II. 5y2 â€“ 7y 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
E) If x = y or relation cannot be established
Solution:

x2 â€“ x â€“ 6 = 0
x2 â€“ 2x + 3x â€“ 6 = 0
So x = -3, 2
5y2 â€“ 7y â€“ 6 = 0
5y2 â€“ 10y + 3y â€“ 6 = 0
So y = -3/5, 2
Put on number line
-3 â€¦. -3/5â€¦.. 2
5. I. 3x2 â€“ 10x + 8 = 0,
II. 3y2 + 8y â€“ 16 = 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
C) If x â‰¥ y
Solution:

3x2 â€“ 10x + 8 = 0
3x2 â€“ 6x â€“ 4x + 8 = 0
So x = 2, 4/3
3y2 + 8y â€“ 16 = 0
3y2 + 12y â€“ 4y â€“ 16 = 0
So y = -4, 4/3
Put on number line
-4 â€¦. 4/3â€¦. 2
6. I. 2x2 + 17x + 30 = 0,
II. 2y2 + 13y + 18 = 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
E) If x = y or cannot be established
Solution:

2x2 + 17x + 30 = 0
2x2 + 12x + 5x + 30 = 0
So x = -6, -5/2
2y2 + 13y + 18 = 0
2y2 + 4y + 9y + 18 = 0
So y = -9/2, -2
Put on number line
-6 â€¦ -9/2 â€¦. -5/2 â€¦. -2
7. I. 3x2 + 16x + 20 = 0,
II. 3y2 + 8y + 4 = 0

A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relationship cannot be determined
D) If x â‰¤ y
Solution:

3x2 + 16x + 20 = 0
3x2 + 6x + 10x + 20 = 0
So x = -10/3, -2
3y2 + 8y + 4 = 0
3y2 + 6y + 2y + 4 = 0
So y = -2, -2/3
put on number line
-10/3â€¦. -2â€¦. -2/3
8. I. x2 + x â€“ 20 = 0,
II. 2y2 + 13y + 15 = 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
E) If x = y or relation cannot be established
Solution:

x2 + x â€“ 20 = 0
(x+5)(x-4) = 0
So x = -5, 4
2y2 + 13y + 15 = 0
2y2 + 10y + 3y + 15 = 0
So y = -5, -3/2
Put on number line
-5â€¦. -3/2â€¦. 4
9. I. 5x2 â€“ 7x â€“ 6 = 0,
II. 5y2 + 23y + 12 = 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
C) If x â‰¥ y
Solution:

5x2 â€“ 7x â€“ 6 = 0
5x2 â€“ 10x + 3x â€“ 6 = 0
So x = -3/5, 2
5y2 + 23y + 12 = 0
5y2 + 20y + 3y + 12 = 0
So y = -4, -3/5
Put on number line
-4â€¦.. -3/5â€¦. 2
10. I. 2x2 – 9x + 4 = 0,
II. 2y2 + 7y – 4 = 0

A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relationship cannot be determined
C) If x â‰¥ y
Solution:

2x2 – 9x + 4 = 0
2x2 – 8x – x + 4 = 0
So x = 4 , 1/2
2y2 + 7y – 4 = 0
2y2 + 8y â€“ y â€“ 4 = 0
So y = -4, 1/2
Put on number line
-4â€¦â€¦. 1/2â€¦â€¦ 4

## 3 Thoughts to “Quantitative Aptitude: Quadratic Equations Set 1”

1. Chotu D(mind) !! {NONSENSE}

done

2. Laughing tym its nitrous oxide

TQ:)

3. Ayushi Srivastava

ty mam