Quantitative Aptitude: Quadratic Equations Set 6

April 15, 2024 infoalfabanker

I. 3x² + 23x + 30 = 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

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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
-6…. -5/3….. -2/3…… 2
I. 3x² – 5x – 12 = 0
II. 3y² + 16y + 16 = 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:
3x² – 5x – 12 = 0
3x² – 9x + 4x – 12 = 0
Gives x = -4/3, 3
3y² + 16y + 16 = 0
3y² + 12y + 4y + 16 = 0
Gives y = -4, -4/3
Put all values on number line and analyze the relationship
-4….. -4/3….. 3
I. 4x² + 17x + 18 = 0
II. 4y² – 3y – 27 = 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 + 17x + 18 = 0
4x² + 8x + 9x + 18 = 0
Gives x = -2, -9/4
4y² – 3y – 27 = 0
4y² – 12y + 9y – 27 = 0
Gives y = -9/4, 3
Put all values on number line and analyze the relationship
-9/4…… -2…… 3
I. 3x² – x – 24 = 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

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Option E
Solution:
3x² – x – 24 = 0
3x² – 9x + 8x – 24 = 0
Gives x = -8/3, 3
4y² + 5y – 6 = 0
4y² + 8y – 3y – 6 = 0
Gives y = -2, 3/4
Put all values on number line and analyze the relationship
-8/3…… -2….. 3/4…… 3
I. 4x² – 9x – 9 = 0
II. 2y² + 17y + 35 = 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:
4x² – 9x – 9 = 0
4x² – 12x + 3x – 9 = 0
Gives x = 3, -3/4
2y² + 17y + 35 = 0
2y² + 10y + 7y + 35 = 0
Gives y = -7/2, -5
Put all values on number line and analyze the relationship
-5……. -7/2…… -3/4….. 3
I. 3x² + 2x – 21 = 0
II. 6y² – 5y – 21 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

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Option E
Solution:
3x² + 2x – 21 = 0
3x² + 9x – 7x – 21 = 0
Gives x = -3, 7/3
6y² – 5y – 21 = 0
6y² + 9y – 14y – 21 = 0
Gives y = -3/2, 7/3
Put all values on number line and analyze the relationship
-3….. -3/2….. 7/3
I. 15x² – 29x + 12 = 0
II. 15y² – 22y + 8 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

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Option E
Solution:
15x² – 29x + 12 = 0
15x² – 9x – 20x + 12 = 0
Gives x = 3/5, 4/3
15y² – 22y + 8 = 0
15y² – 10y – 12y + 8 = 0
Gives y = 4/5, 2/3
Put all values on number line and analyze the relationship
3/5….. 2/3….. 4/5…. 4/3
I. 4x² + 9x – 9 = 0
II. 4y² – 19y + 12 = 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:
4x² + 9x – 9 = 0
4x² + 12x – 3x – 9 = 0
Gives x = -3, 3/4
4y² – 19y + 12 = 0
4y² – 16y – 3y + 12 = 0
Gives y = 3/4, 4
Put all values on number line and analyze the relationship
-3…….. 3/4….. 4
I. 3x² + 19x + 28 = 0
II. 3y² + 13y + 14 = 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 + 19x + 28 = 0
3x² + 12x + 7x + 28 = 0
Gives x = -4, -7/3
3y² + 13y + 14 = 0
3y² + 6y + 7y + 14 = 0
Gives y = -7/3, -2
Put all values on number line and analyze the relationship
-4…… -7/3…… -2
I. 2x² – 19x + 42 = 0
II. 3y² – 13y + 12 = 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:
2x² – 19x + 42 = 0
2x² – 12x – 7x + 42 = 0
Gives x = 7/2, 6
3y² – 13y + 12 = 0
3y² – 9y + 4y + 12 = 0
Gives y = 4/3, 3
Put all values on number line and analyze the relationship
4/3…… 3…… 7/2….. 6

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