# Quantitative Aptitude: Quadratic Equations Set 9

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. 8/âˆšx + 9/(âˆšx +1) = 7,
II. 9/âˆšy â€“ 3/âˆšy = 2
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:

8/âˆšx + 9/(âˆšx +1) = 7
[8(âˆšx +1) + 9âˆšx]/[âˆšx * (âˆšx +1)] = 7
17âˆšx + 8 = 7 (x + âˆšx)
7x – 10âˆšx â€“ 8 = 0
7x – 14âˆšx + 4âˆšx â€“ 8 = 0
7âˆšx (âˆšx â€“ 2) + 4 (âˆšx â€“ 2) = 0
âˆšx cannot be -4/7
So âˆšx = 2, so x = 4
9/âˆšy â€“ 3/âˆšy = 2
(9 – 3)/âˆšy = 2
Gives âˆšy = 3, so y = 9
2. I. 9/âˆšx + 3/âˆšx = âˆšx + 1,
II. 4y2 + 5y â€“ 6 = 0
A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) x = y or relation cannot be established
Option A
Solution:

9/âˆšx + 3/âˆšx = âˆšx + 1
12/âˆšx = âˆšx + 1
x + âˆšx â€“ 12 = 0
x + 4âˆšx – 3âˆšx â€“ 12 = 0
âˆšx(âˆšx + 4) â€“ 3 (âˆšx + 4) = 0
âˆšx cannot be -4, So âˆšx = 3 => x = 9
4y2 + 5y â€“ 6 = 0
4y2 + 5y â€“ 6 = 0
Gives y = -2, 3/4
Put all values on number line and analyze the relationship
-2â€¦ 3/4â€¦ 9
3. I. 6x2 + 13x + 6 = 0,
II. 6y2 â€“ y â€“ 2 = 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:

6x2 + 13x + 6 = 0
6x2 + 9x + 4x + 6 = 0
Gives x = -2/3, -3/2
6y2 â€“ y â€“ 2 = 0
6y2 + 3y â€“ 4y â€“ 2 = 0
Gives y = -1/2, 2/3
Put all values on number line and analyze the relationship
-3/2â€¦ -2/3â€¦ -1/2â€¦ 2/3
4. I. 3x2 + 14x â€“ 5 = 0,
II. 3y2 â€“ 11y + 6 = 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 + 14x â€“ 5 = 0
3x2 + 15x â€“ x â€“ 5 = 0
Gives x = -5, 1/3
3y2 â€“ 11y + 6 = 0
3y2 â€“ 9y â€“ 2y + 6 = 0
Gives y = 2/3, 3
Put all values on number line and analyze the relationship
-5â€¦ 1/3â€¦ 2/3â€¦ 3
5. I. 6x2 + 5x â€“ 1 = 0,
II. 3y2 â€“ 10y + 3 = 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:

6x2 + 5x â€“ 1 = 0
6x2 + 6x â€“ x â€“ 1 = 0
Gives x = -1, 1/6
3y2 â€“ 10y + 3 = 0
3y2 â€“ 9y â€“ y + 3 = 0
Gives y = 1/3, 3
Put all values on number line and analyze the relationship
-1â€¦ 1/6â€¦ 1/3â€¦ 3
6. I. 12x2 â€“ 5x â€“ 3 = 0,
II. 3y2 â€“ 11y + 6 = 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:

12x2 â€“ 5x â€“ 3 = 0
12x2 + 4x â€“ 9x â€“ 3 = 0
Gives x = -1/3, 3/4
3y2 â€“ 11y + 6 = 0
3y2 â€“ 9y â€“ 2y + 6 = 0
Gives y = 2/3, 3
Put all values on number line and analyze the relationship
-1/3â€¦ 2/3â€¦ 3/4â€¦ 3
7. I. 6x2 + 7x + 2 = 0,
II. 15y2 â€“ 38y â€“ 40 = 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:

6x2 + 7x + 2 = 0
6x2 + 4x + 3x + 2 = 0
Gives x = -2/3, -1/2
15y2 â€“ 38y – 40 = 0
15y2 + 12y â€“ 50y – 40 = 0
Gives y = -4/5, 10/3
Put all values on number line and analyze the relationship
-4/5â€¦ -2/3â€¦ -1/2â€¦ 10/3
8. I. 3x2 â€“ 25x + 52 = 0,
II. 2y2 â€“ 7y + 3 = 0
A) x > y
B) x < y
C) x â‰¥ y
D) x â‰¤ y
E) 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
2y2 â€“ 7y + 3 = 0
2y2 â€“ 6y â€“ y + 3 = 0
So y = 1/2, 3
Put all values on number line and analyze the relationship
1/2â€¦ 3â€¦ 4â€¦ 13/3
9. I. x2 = 1156,
II. y = âˆš1156
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:

x2 = 1156,
So x = -34, 34
y = âˆš1156
So y = 34
Put all values on number line and analyze the relationship
-34â€¦ 34
10. I. x2 – âˆš3969 = âˆš6561,
II. y2 – âˆš1296 = âˆš4096
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:

x2 – âˆš3969 = âˆš6561
x2 – 63 = 81
x2 = 144
So x = -12, 12
y2 – âˆš1296 = âˆš4096
y2 – 36 = 64
y2 = 100
So y = -10, 10
Put all values on number line and analyze the relationship
-12â€¦ -10â€¦.10â€¦. 12

## 5 Thoughts to “Quantitative Aptitude: Quadratic Equations Set 9”

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9âˆšx + 3/âˆšx = âˆšx + 1, check 2nd one it has mistake, but correct in solu

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