# Quantitative Aptitude: Quadratic Equations Set 4

### 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. 6x2 + 7x -3 = 0
II. y (10y – 1) = 2
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option E
Solution:

6 x2 + 7x -3 = 0
6 x2 + 9x – 2x – 3 = 0
So x = -1.5, 0.3
y (10y – 1) = 2
10y2 – y – 2 = 0
10y2 – 5y + 4y – 2 = 0
So y = 0.5, -0.4
Put all values on number line and analyze the relationship
-1.5… -0.4… 0.3… 0.5
2. I. 4x2 + 3x – 27 = 0
II. 15y2 – 38y – 21 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option E
Solution:

4x2 + 3x – 27 = 0
4x2 + 12x – 9x – 27 = 0
So x =2.25, -3
15y2 – 38y – 21 = 0
15y2 – 45y + 7y – 21 = 0
So y = 3, – 0.46
Put all values on number line and analyze the relationship
-3… -0.46… 2.25…. 3
3. I. 8x2 + 5x – 13 = 0
II. 2y2 + 23y + 63 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option A
Solution:

8x2 + 5x – 13 = 0
8x2 + 13x – 8x – 13 = 0
So x = -1.625, 1
2y2 + 23y + 63 = 0
2y2 + 14y + 9y + 63 = 0
So y = -7, -4.5
Put all values on number line and analyze the relationship
-7…. -4.5 ….-1.625…. 1
4. I. 4x2 + 19x + 21 = 0
II. 2y2 – 25y – 27 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option B
Solution:

4x2 + 19x + 21 = 0
4x2 + 12x + 7x + 21 = 0,
So x = -3, – 1.75
2y2 – 25y – 27 = 0
2y2 – 27y + 2y – 27 = 0
So y = 13.5, -1
Put all values on number line and analyze the relationship
-3…. -1.75….. -1…..13.5
5. I. x2 – 9x + 20 = 0
II. y2 – 11y + 30 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option D
Solution:

x2 – 9x + 20 = 0
x2 – 4x – 5x + 20 = 0
So x = 4, 5
y2 – 11y + 30 = 0
y2 – 5y -6y + 30 = 0
So y = 5, 6
Put all values on number line and analyze the relationship
4 …. 5….5……6
6. I. x2 – 7x + 12 = 0
II. y2 – 5y + 6 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option C
Solution:

x2 – 7x + 12 = 0
x2 – 3x – 4x + 12 = 0
So x = 3, 4
y2 – 5y + 6 = 0
y2 – 3y – 2y + 6 = 0
So y = 2, 3
Put all values on number line and analyze the relationship
2…. 3….3…. 4
7. I. x2 – 2x – 15 = 0
II. y2 + 22 = 122
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined
Option E
Solution:

x2 – 2x – 15 = 0
x2 – 5x + 3x – 15 = 0
So x = 5, -3
y2 + 22 = 122
y2 = 100
y = + 10, -10
Put all values on number line and analyze the relationship
-10….-3….5….10
8. I. x2 + x – 30 = 0
II. y2 – 11y + 30 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option D
Solution:

x2 + x – 30 = 0
x2 + 6x – 5x – 30 = 0
So x = – 6, 5
y2 – 11y + 30 = 0
y2 – 5y – 6y + 30 = 0
So y = 5, 6
Put all values on number line and analyze the relationship
-6…. 5…. 5… 6
9. I. 2 + 5x – 14 = 0
II. y2 + 24y + 128 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established
Option A
Solution:

x2 + 5x – 14 = 0
x2 + 7x – 2x – 14 = 0
So x = -7, 2
y2 + 24y + 128 = 0
y2 + 16y + 8y + 128 = 0
So y = -16, -8
Put all values on number line and analyze the relationship
-16…..-8….. -7….2
10. I. x2 – 6x – 91 = 0
II. y2 – 32y + 247 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined
Option D
Solution:

x2 – 6x – 91 = 0
x2 – 13x + 7x – 91 = 0
So x = 13, -7
y2 – 32y + 247 = 0
y2 – 19y -13y + 247 = 0
So y = 19, 13
Put all values on number line and analyze the relationship
-7…13…13…19

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