Question

You are given a pair of statements.

1. N is a perfect square.

2. M is a perfect cube.

Which of the following questions can be answered by using the given statements?

1. Is M × N a perfect square?
2. Is M × N a perfect Cube?
3. Is M × N a prime?
4. Is M × N greater than 1000?

Answer 1

Correct Answer - Option 3 : Is M × N a prime?

The logic followed is:

The given pair of statements is 

1. N is a perfect square.

2. M is a perfect cube.

Unless we don't know the value of N and M we can't make a decision on whether their product is a perfect square or perfect cube or it is greater than 1000.

But we can say that the product of M and N cannot be a prime number. Because the product is divisible by N and M individually.

Let's take an example to understand this concept.

Suppose N = 4 and M = 125

4 is a perfect square and 125 is a perfect cube.

Then,

⇒ 4 × 125 = 500

500 is neither the perfect square nor is the perfect cube nor it is greater than 1000.

But 500 is not a prime number, So we can definitely answer the question "Is M × N a prime?", which is not true. 

Hence, the correct answer is Option 3).