Question: Is m > n if m, n are real numbers?

Statement-I:

m = (1 - p) (p2 + p + 1) and

n = (p + 1) (p2 - p + 1)

Statement-II:

m = pn

Question

Question

This question was previously asked in

CDS Elementary Mathematics 3 Sep 2023 Official Paper

if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
if the question can be answered by using either statement alone.
if the question can be answered by using both the statements together, but cannot be answered using either statement alone.
if the question cannot be answered even by using both the statements together.

Answer 1

Given:

Statement 1

m = (1 - p) (p2 + p + 1)

n = (p + 1) (p2 - p + 1)

Statement 2

m = pn

Formula:

a³ - b³= (a - b) (a² + b² + ab)

a³ + b³ = (a + b)(a² + b² - ab)

Calculation:

Statement: 1

m = (1 - p) (p2 + p + 1)

By using the above identities

m = (1 - p3)

n = (p + 1) (p2 - p + 1)

By using the above identities

n = (p3 + 1)

Since, we don't know wether p is +ve, -ve, integer or fraction

We can not conclude the relation on m & n

Statement: 2 m = pn

Here also, relation b/w m & n depend on only P. therefore

∴ The correct answer is option D.

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