Q. Four runners - Ravi, Sahil, Tarun, and Uday - run at different speeds.
Who is the fastest?
(I) Tarun runs faster than Ravi but slower than Sahil.
(II) Uday runs slower than Sahil but faster than Tarun.
Analyzing Runner Speeds Using Data Sufficiency
The question asks to identify the fastest runner among Ravi, Sahil, Tarun, and Uday, given that they all run at different speeds.
Evaluating Statement (I)
Statement (I) provides the following information:
- Tarun runs faster than Ravi (\(T > R\)).
- Tarun runs slower than Sahil (\(S > T\)).
Combining these, we get the order: \(S > T > R\). This tells us Sahil is faster than Tarun, and Tarun is faster than Ravi. However, Uday's position relative to Sahil is unknown. Uday could potentially be faster than Sahil. Therefore, Statement (I) alone is insufficient.
Evaluating Statement (II)
Statement (II) provides the following information:
- Uday runs slower than Sahil (\(S > U\)).
- Uday runs faster than Tarun (\(U > T\)).
Combining these, we get the order: \(S > U > T\). This tells us Sahil is faster than Uday, and Uday is faster than Tarun. However, Ravi's position relative to Sahil is unknown. Ravi could potentially be faster than Sahil. Therefore, Statement (II) alone is insufficient.
Evaluating Statements (I) and (II) Together
Combining the information from both statements:
- From Statement (I): \(S > T > R\)
- From Statement (II): \(S > U > T\)
Synthesizing these inequalities:
- We know \(S > U\) (from II).
- We know \(U > T\) (from II).
- We know \(T > R\) (from I).
Combining all parts gives the complete order: \(S > U > T > R\).
This combined order clearly shows that Sahil (\(S\)) is the fastest runner among the four.
Therefore, data in both statements I and II together are sufficient to answer the question.
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Important Questions from Data Sufficiency
Consider two Statements and a Question:
Statement 1: Priya is 4 ranks below Seema and is 31 st from the bottom.
Statement 2: Ena is 2 ranks above Seema and is 37" from the bottom.
Question: What is Seema’s rank from the top in the class of 40 students ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question:
Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the-heaviest.
Statement 2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A,B,C, D and E?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider the Question and two Statements given below :
Question : Is xan integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3 xis an integer.
Which one of the following is correct in respect of the Question and the Statements?
Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5.
Which one of the following is correct in respect of the Question and the Statements?
