Consider the question: Who among P, Q, R, S and T is the lightest in weight? Use the following statements and decide which combination of statements is sufficient to answer the question. 1. Q is lighter than P and S, and S is heavier than T. 2. R is heavier than Q but lighter than T.

Introduction / Context:
This is a data sufficiency question. Rather than asking for the exact lightest person directly, it asks which given statements are enough to determine who is the lightest. The main task is to decide sufficiency, not to compute the exact weights. This skill is highly valued in management and bank exams where quick logical decisions are needed.

Given Data / Assumptions:

• We have five people: P, Q, R, S and T.
• Question: Who is the lightest in weight?
• Statement 1: Q is lighter than P and S, and S is heavier than T.
• Statement 2: R is heavier than Q but lighter than T.

Concept / Approach:
For data sufficiency, we test each statement alone and then both together. A statement or a pair of statements is sufficient if it lets us answer the question uniquely. If more than one person can be the lightest under a statement without breaking the given conditions, then that statement is not sufficient by itself.

Step-by-Step Solution:
Step 1: Use statement 1 alone. From statement 1, Q is lighter than P and S. Also, S is heavier than T, so T is lighter than S. From this, we can deduce partial orderings like Q < P, Q < S, and T < S. However, we do not know any relation between Q and T or between R and any of the others. So the lightest person could be Q or T or even R, depending on their exact weights. Statement 1 alone is not sufficient. Step 2: Use statement 2 alone. Statement 2 tells us that R is heavier than Q but lighter than T. So Q < R < T. There is no information about P or S here, so the lightest could be Q or perhaps P or S if they are lighter than Q. Hence statement 2 by itself is also not sufficient. Step 3: Combine statements 1 and 2. From statement 1 we know Q < P and Q < S and T < S. From statement 2 we know Q < R < T. Combining these, we have Q lighter than P, R, S and T. T is lighter than S but heavier than R and Q. There is no way for any person other than Q to be the lightest without violating the relations. Thus, using both statements together, Q is uniquely determined as the lightest person.

Verification / Alternative check:
Try to construct a numeric example that respects both statements. Choose Q = 1, R = 2, T = 3, S = 4 and P = 5 in arbitrary units. All conditions are satisfied: Q is lighter than P and S, S is heavier than T, and R is between Q and T. In this example Q is clearly the lightest. Any attempt to make another person lighter than Q will break one of the given inequalities. Therefore the combination of both statements is sufficient to answer the question.

Why Other Options Are Wrong:

• Option a and option b are wrong because neither statement alone determines the lightest person.
• Option d is wrong because the two statements together do provide a unique answer.
• Option e is wrong since each statement alone is not sufficient.

Common Pitfalls:
Students often confuse partial order with complete order. Just because a statement compares some people, it does not mean the complete ranking is known. Always check whether every person in the list has a fixed place relative to the others before declaring sufficiency.

Final Answer:
Both statements 1 and 2 together are sufficient, so option c is correct.