Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. 0 < x < 1 Quantity A: (3x3 - 9x) (5x + 7) Quantity B: (3x2 + 9) (5x2 + 7x)

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

0 < x < 1

Quantity A: (3x³ - 9x) (5x + 7)

Quantity B: (3x² + 9) (5x² + 7x)

A Quantity A > Quantity B

B Quantity A < Quantity B

C Quantity A ≥ Quantity B

D Quantity A ≤ Quantity B

E Quantity A = Quantity B OR relationship cannot be determined.

Solution

Correct Answer: Option B

Notice that in each of the quantities, we can factor 3x out of the given expressions.

0 < x < 1

Quantity A: (3x³ - 9x) (5x + 7) = 3x(x² - 3) (5x + 7)

Quantity B: (3x² + 9) (5x² + 7x) = 3x(x² + 3) (5x + 7)

Because we know that x is not 0, we can divide away 3x from both quantities.

Also, 0 < x < 1, so (5x + 7) ≠ 0, we can divide away (5x + 7) from both quantities as well.

Quantity A: 3x(x² - 3) (5x + 7) = x² - 3

Quantity B: 3x(x² + 3) (5x + 7) = x² + 3

Since x² will always be positive, (x² + 3) will always be bigger than (x² – 3).

Solution

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