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

This question was previously asked in
CDS Elementary Mathematics 3 Sep 2023 Official Paper
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  1. if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
  2. if the question can be answered by using either statement alone.
  3. if the question can be answered by using both the statements together, but cannot be answered using either statement alone.
  4. if the question cannot be answered even by using both the statements together.

Answer (Detailed Solution Below)

Option 4 : if the question cannot be answered even by using both the statements together.
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Detailed Solution

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Given:

Statement 1

m = (1 - p) (p2 + p + 1)

n = (p + 1) (p2 - p + 1)

Statement 2

m = pn

Formula:

a3 - b= (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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