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. Quantity A: If a number is as much greater than 53 as it is less than 175, then the number: Quantity B: If \(p = \frac{{5 - {q^2}}}{{p - q}}\) and the value of p3 + q3 = 45 then the value of (p + q)3/2:

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.

Quantity A: If a number is as much greater than 53 as it is less than 175, then the number:

Quantity B: If \(p = \frac{{5 - {q^2}}}{{p - q}}\) and the value of p³ + q³ = 45 then the value of (p + q)^3/2:

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

Solution

Correct Answer: Option A

First we will find Quantity A,

Quantity A:

Let the number be ‘x’.

(x – 53) = (175 – x)

⇒ x + x = 175 + 53

⇒ x = 228/2 = 114

∴ x = 114

Now,

Quantity B:

\(p = \frac{{5 - {q^2}}}{{p - q}}\)

⇒ p (p – q) = 5 – q²

⇒ p² – pq + q² = 5

⇒ (p² – pq + q²) = 5

We know that,

a³ + b³ = (a + b)(a² – ab + b²)

Now,

p³ + q³ = (p + q)(p² – pq + q²)

⇒ 45 = (p + q) × 5

⇒ (p + q) = 45/5 = 9

∴ (p+q)^3/2 = 9^3/2 = 27

∴ Quantity A > Quantity B

Solution

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