Understanding the Lightest Person Question

The question asks us to determine who among five people (P, Q, R, S, and T) is the lightest, based on information provided in two statements. We need to figure out if one statement alone, or both statements together, are sufficient to answer this question.

Analyzing Statement 1 for Weight Comparison

Statement 1 says: "Q weight < P and S also S weight > T".

Let's break this down into individual inequalities:

• Q weight < P means Q is lighter than P, or \(Q < P\).
• Q weight < S means Q is lighter than S, or \(Q < S\).
• S weight > T means S is heavier than T, or \(S > T\), which is the same as \(T < S\).

Combining these, we know:

• \(Q < P\)
• \(Q < S\)
• \(T < S\)

From statement 1, we know Q is lighter than both P and S. We also know T is lighter than S. However, we don't know the relationship between Q and T, or between any of these people and R. For example, Q could be lighter than T, or T could be lighter than Q, or they could even have the same weight relative to the others based on this statement alone. Therefore, statement 1 alone is not sufficient to find the lightest person among all five.

Analyzing Statement 2 for Weight Comparison

Statement 2 says: "R weight > Q but < T".

Let's break this down:

• R weight > Q means R is heavier than Q, or \(R > Q\), which is the same as \(Q < R\).
• R weight < T means R is lighter than T, or \(R < T\).

Combining these, we get a sequence: \(Q < R < T\). This means Q is lighter than R, and R is lighter than T. Consequently, Q is also lighter than T.

From statement 2 alone, we know the relative weights of Q, R, and T. Q is the lightest among these three. However, we don't know the relationship between Q, R, T and P or S. We cannot determine the absolute lightest person among all five using only statement 2. Therefore, statement 2 alone is not sufficient to find the lightest person.

Combining Both Statements to Find the Lightest

Now let's combine the information from both statements.

From statement 1, we have:

• \(Q < P\)
• \(Q < S\)
• \(T < S\)

From statement 2, we have:

• \(Q < R\)
• \(R < T\)

Let's put the sequence from statement 2 together with the information from statement 1.

We know \(Q < R < T\).

From statement 1, we know \(T < S\). So, we can extend the sequence: \(Q < R < T < S\). This tells us that among Q, R, T, and S, Q is the lightest.

Also from statement 1, we know \(Q < P\). This tells us Q is lighter than P.

So, we have established that Q is lighter than R, Q is lighter than T, Q is lighter than S, and Q is lighter than P. This means Q is lighter than all other four people (P, R, S, and T).

Therefore, by combining both statements, we can definitively determine that Q is the lightest person.

Since both statements together are needed to answer the question, the information provided is sufficient only when both statements are used.

Summary of Statement Sufficiency

Let's summarize the sufficiency of each statement and their combination:

Based on this analysis, neither statement alone is sufficient, but both statements together are sufficient to answer the question "Who among P, Q, R, S and T is lightest in weight?".

Revision Table: Weight Comparison Logic

Additional Information: Data Sufficiency Problems

Data sufficiency questions are common in logical reasoning and analytical sections of exams. They test your ability to analyze given information and determine if it is sufficient to answer a specific question. Here are some key points to remember:

• Analyze each statement separately first: Determine if statement 1 alone is sufficient. Then, determine if statement 2 alone is sufficient. Ignore the other statement while analyzing one.
• Do not assume anything: Only use the information explicitly given in the statements and the question.
• Combine statements if necessary: If neither statement alone is sufficient, combine the information from both statements and see if they together can answer the question.
• Identify the minimum required information: The goal is to find which statement(s) provide *just enough* information to get a single, definite answer to the question asked.
• Possible Outcomes: The typical options in data sufficiency questions reflect the different possible conclusions: Statement 1 alone is sufficient, Statement 2 alone is sufficient, Both statements are sufficient, Neither statement is sufficient.

In this specific question about weights, the statements provide relative comparisons. By carefully combining these relative comparisons, we could establish a complete order for some individuals and then determine the lightest among all five.