A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Is ${(p+q)}^2-4pq$, where p, q are natural numbers, positive?
Statement I: p < q.
Statement II: p > q.
Which one of the following is correct in respect of the above Question and the Statements?

Correct Option: The Question can be answered by using either Statement alone.

Step 1: Simplify the given algebraic expression in the Question

We are asked to determine whether the expression given below is positive:

${(p+q)}^2-4pq$

Expanding ${(p+q)}^2$ using the algebraic identity ${(a+b)}^2=a^2+2ab+b^2$:

${(p+q)}^2-4pq=p^2+2pq+q^2-4pq$

$=p^2-2pq+q^2$

$={(p-q)}^2$

So, the question simplifies to: Is ${(p-q)}^2>0$?

Step 2: Analyze the conditions for the expression to be positive

The square of any non-zero real number is always strictly positive. Since p and q are natural numbers, ${(p-q)}^2$ will be greater than 0 as long as $p-q\ne 0$ (i.e., $p\ne q$).

Step 3: Evaluate Statement I

Statement I gives: $p<q$.

If $p<q$, then $p-q$ is a non-zero negative number.

Squaring any non-zero negative number results in a positive number. Hence, ${(p-q)}^2>0$.

Thus, Statement I alone is sufficient to answer the Question definitively with a "Yes".

Step 4: Evaluate Statement II

Statement II gives: $p>q$.

If $p>q$, then $p-q$ is a non-zero positive number.

Squaring any positive number results in a positive number. Hence, ${(p-q)}^2>0$.

Thus, Statement II alone is also sufficient to answer the Question definitively with a "Yes".

Conclusion:

Since either statement independently provides enough information to conclusively answer the question, the correct choice is: "The Question can be answered by using either Statement alone."