Quant - Quadratic Test 488

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Question 1/5
1 / -0.25

Directions For Questions

Direction: In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

...view full instructions

I. 2x²+ 3x – 20 = 0
II. 2y² – y – 21 = 0

Correct

Wrong

Skipped
A
x > y

Correct

Wrong

Skipped
B
x ≥ y

Correct

Wrong

Skipped
C
x < y

Correct

Wrong

Skipped
D
x ≤ y

Correct

Wrong

Skipped
E
x = y or no relationship can be established between x and y

Solutions

I. 2x²+ 3x – 20 = 0

⇒ 2x²+ 8x – 5x – 20 = 0

⇒ 2x(x + 4) – 5(x + 4) = 0

⇒ (2x – 5)(x + 4) = 0

⇒ x = –4 and 2.5

II. 2y² – y – 21 = 0

⇒ 2y² + 6y – 7y – 21 = 0

⇒ 2y(y + 3) – 7(y + 3) = 0

⇒ (y + 3)(2y – 7) = 0

⇒ y = –3 and 3.5

∴ No relationship can be established between x and y.
Question 2/5
1 / -0.25

Directions For Questions

Direction: In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

...view full instructions

I. x²− 12x + 35 = 0
II. y²− 13y + 40 = 0

Correct

Wrong

Skipped
A
x < y

Correct

Wrong

Skipped
B
x > y

Correct

Wrong

Skipped
C
x ≤ y

Correct

Wrong

Skipped
D
x ≥ y

Correct

Wrong

Skipped
E
x = y or no relationship can be established between x and y.

Solutions

I. x²− 12x + 35 = 0

⇒ (x²− 5x) – (7x − 35) = 0

⇒ x(x − 5) – 7(x − 5) = 0

⇒ (x − 7)(x − 5) = 0

⇒ x = 5 and 7

II. y²− 13y + 40 = 0

⇒ (y²– 5y) – (8y – 40) = 0

⇒ y(y – 5) – 8(y – 5) = 0

⇒ (y − 5)(y – 8) = 0

⇒ y = 5 and 8
Now, (x = 5) < (y = 8)
And, (x = 7) > (y = 5)

Thus, no relationship can be established between x and y.
Question 3/5
1 / -0.25

Directions For Questions

Direction: In the following question two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

...view full instructions

I. x² + 6x − 55 = 0
II. y²− 5y – 36 = 0

Correct

Wrong

Skipped
A
x < y

Correct

Wrong

Skipped
B
x > y

Correct

Wrong

Skipped
C
x ≤ y

Correct

Wrong

Skipped
D
x ≥ y

Correct

Wrong

Skipped
E
x = y or no relationship can be established between x and y.

Solutions

x² + 6x − 55 = 0

⇒ (x²− 5x) + (11x − 55) = 0

⇒ x(x − 5) + 11(x − 5) = 0

⇒ (x + 11)(x − 5) = 0

⇒ x = 5 and −11

y²− 5y – 36 = 0

⇒ (y²+ 4y) – (9y + 36) = 0

⇒ y(y + 4) – 9(y + 4) = 0

⇒ (y + 4)(y – 9) = 0

⇒ y = 9 and −4

∴ No relationship can be established between x and y.
Question 4/5
1 / -0.25

Directions For Questions

Direction: In the following question two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

...view full instructions

I. x² + 12x + 35 = 0
II. y² + y - 20 = 0

Correct

Wrong

Skipped
A
x > y

Correct

Wrong

Skipped
B
x ≥ y

Correct

Wrong

Skipped
C
x < y

Correct

Wrong

Skipped
D
x ≤ y

Correct

Wrong

Skipped
E
x = y or no relationship can be established between x and y

Solutions

x² + 12x + 35 = 0

(x² + 7x) + (5x + 35) = 0

x(x + 7) + 5(x + 7) = 0

(x + 5)(x + 7) = 0

x = –7, –5

y² + y - 20 = 0

(y² - 4y) + (5y - 20) = 0

y(y- 4) + 5(y - 4) = 0

(y + 5)(y - 4) = 0

y = 4 and –5

∴ x ≤ y
Question 5/5
1 / -0.25

Directions For Questions

Direction: In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

...view full instructions

I. x² – 14x + 48 = 0
II. y² + 14y + 48 = 0

Correct

Wrong

Skipped
A
x > y

Correct

Wrong

Skipped
B
x ≥ y

Correct

Wrong

Skipped
C
x < y

Correct

Wrong

Skipped
D
x ≤ y

Correct

Wrong

Skipped
E
x = y or no relationship can be established between x and y

Solutions

x² – 14x + 48 = 0

(x²- 6x) - (8x - 48) = 0

x(x - 6) - 8(x - 6) = 0

(x - 6)(x - 8) = 0

x = 6 and 8

y² + 14y + 48 = 0

(y² + 6y) + (8y + 48 ) = 0

y(y+6) + 8(y + 6) = 0

(y + 6)(y + 8) = 0

y = –6 and –8

∴ x > y

Question 1/5

x > y

x ≥ y

x < y

x ≤ y

x = y or no relationship can be established between x and y

Question 2/5

x < y

x > y

x ≤ y

x ≥ y

x = y or no relationship can be established between x and y.

Question 3/5

x < y

x > y

x ≤ y

x ≥ y

x = y or no relationship can be established between x and y.

Question 4/5

x > y

x ≥ y

x < y

x ≤ y

x = y or no relationship can be established between x and y

Question 5/5

x > y

x ≥ y

x < y

x ≤ y

x = y or no relationship can be established between x and y