Question

What is the present age of the person P? Statements: (I) \(P\) is four years older than another person \(Q\). (II) \(Q\) is two years younger than another person \(R\).

• A. Statement (I) alone is sufficient to answer the question, but (II) alone is not sufficient.
• B. Statement (II) alone is sufficient to answer the question, but (I) alone is not sufficient.
• C. Both the statements (I) and (II) are sufficient to answer the question, but neither statement alone is sufficient.
• D. Both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.

Hint:

In age problems, relations alone are not enough for exact age. At least one fixed age value is necessary.

Answer 1

The Correct Option is D

Concept: To determine the present age of a person, at least one actual numerical age must be known. If only relationships between ages are given, exact age cannot be found.

Step 1: Checking Statement (I).
Given: \[ P=Q+4 \] This gives only the relation between \(P\) and \(Q\). But the exact age of \(Q\) is unknown. So, the exact age of \(P\) cannot be found. Thus, Statement (I) alone is not sufficient.

Step 2: Checking Statement (II).
Given: \[ Q=R-2 \] This gives only the relation between \(Q\) and \(R\). There is no direct relation with \(P\). So, Statement (II) alone is not sufficient.

Step 3: Checking both statements together.
From Statement (I): \[ P=Q+4 \] From Statement (II): \[ Q=R-2 \] Substituting: \[ P=(R-2)+4 \] \[ P=R+2 \] Still, no actual age of \(R\) is given. So the exact age of \(P\) cannot be determined. Hence, additional information is required.