Consider the given question and decode which of the following statements is sufficient to answer the question. Who among P, Q, R, S and T is lightest in weight? Statements: 1. Q weight < P and S also S weight > T 2. R weight > Q but < T
Both statement 1 and 2 are sufficient.
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:
| Statement(s) | Information Gained | Sufficient to Find Lightest? |
|---|---|---|
| Statement 1 Alone | \(Q < P\), \(Q < S\), \(T < S\) | No |
| Statement 2 Alone | \(Q < R < T\) | No |
| Statements 1 and 2 Combined | \(Q < P\), \(Q < R\), \(Q < T\), \(Q < S\) (derived) | Yes |
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
| Concept | Explanation | Application in Question |
|---|---|---|
| Inequalities | Representing relationships like 'greater than' (>) and 'less than' (<). | Translating statements into \(Q < P\), \(S > T\), \(R > Q\), \(R < T\). |
| Combining Inequalities | Linking multiple inequalities to establish a sequence or overall relationship (e.g., \(a < b\) and \(b < c\) implies \(a < c\)). | Combining \(Q < R\) and \(R < T\) to get \(Q < T\). Combining \(Q < T\) and \(T < S\) to get \(Q < S\). |
| Data Sufficiency | Determining if the given information is enough to answer a specific question. | Evaluating if statement 1, statement 2, or both together provide enough detail to identify the lightest person. |
| Logical Deduction | Drawing necessary conclusions from given premises. | Concluding that Q is the lightest because it is lighter than every other individual mentioned in the combined statements. |
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.
Similar Questions
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Important Questions from Data Sufficiency
Please read the below equation and select an appropriate option from the following.
x + y = 10 ; y = x - 2
Quantity A is x.
Quantity B is y.
A lady wants to buy the following items in the given price range-
1. Tomato between Rs. 40 and Rs. 45 per kg.
2. Grapes in the price range of Rs. 80 and Rs. 90 per kg.
3. Milk packets at Rs. 23 per liter.
In which shop from the following will she definitely get all her items/
A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter.
B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg.
C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg.
D. Shop P sells tomato at Rs. 23.5 per half kg, grapes at Rs. 85 per kg and milk at Rs. 23 per litre.You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
When is Yuvi's wedding anniversary?
Statements:
1: On the 7 th day of a month.
2. The month has 29 days only in a leap year.
One question and three statements are numbered (I), (II) and (III). You have to decide whether the facts given in the statements are sufficient to answer the question given below.
Question: What is the length of the rectangle?
Statement:
I. The perimeter of the rectangle is 80 meters.
II. The sum of the adjacent sides is 40 meters.
III. The width of the rectangle is 10 meters.
Choose the correct option.
A. Only I is sufficient.
B. Only I and II are sufficient.
C. III and one from I or II are sufficient.
D. II and one from I or III are sufficient.
A question and three statements are numbered (I), (II) and (III). You have to decide whether the facts given in the statements are sufficient to answer the question given below.
Question: Five people A, B, C, D and E are sitting facing each other in a circle. E is seated between whom?
Statement:
I. The person sitting to the left of B and to the right of A is the same.
II. D is to the right of B.
III. A sits between E and C.
Choose the correct option.
A. Only I and II are sufficient.
B. Only I and III are sufficient.
C. Only III is sufficient.
D. Facts are insufficient.
