Question:
Among 5 trees, L, M, N, T and V each having a different height, which tree is the shortest?
Statements:
(I) N is shorter than only three trees.
(II) N is taller than M but shorter than T.
Analysis of Statement (I)
Statement (I) states: "N is shorter than only three trees."
- There are 5 trees in total (L, M, N, T, V).
- If N is shorter than exactly 3 trees, it means there are 3 trees taller than N.
- This places N as the 4th tallest tree.
- Consequently, there must be exactly one tree shorter than N.
- However, Statement (I) does not identify which specific tree among L, M, T, or V is the shortest one.
- Conclusion: Statement (I) alone is not sufficient to determine the shortest tree.
Analysis of Statement (II)
Statement (II) states: "N is taller than M but shorter than T."
- This provides a partial order: M < N < T.
- This statement does not give information about the heights of trees L and V relative to M, N, or T.
- For example, L could be shorter than M, making L the shortest tree overall.
- Conclusion: Statement (II) alone is not sufficient to determine the shortest tree.
Analysis of Statements (I) and (II) Together
Let's combine the information from both statements:
- From Statement (I), we know N is the 4th tallest tree, implying exactly one tree is shorter than N.
- From Statement (II), we know M is shorter than N (M < N).
- Since M is shorter than N, and Statement (I) confirms only one tree is shorter than N, M must be that single shortest tree.
- Therefore, combining both statements allows us to definitively conclude that M is the shortest tree.
- Conclusion: Both statements together are sufficient.
Final Decision
Based on the analysis, neither Statement (I) nor Statement (II) alone is sufficient to answer the question. However, when considered together, they provide enough information to identify the shortest tree.
This matches the condition for Option D.
Important Questions from Data Sufficiency
- In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.
Q. Harsh, Ketan, Mayank, Rohit, and Sidharth, each have different height. Who is the shortest?
(I) Mayank is taller than Harsh but shorter than Ketan.
(II) Rohit is taller than Harsh but shorter than Mayank. - In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.
Q. Kunal, Mohit, Rohan, Sandeep, and Tarun - each have different age. Who is the oldest?
(I) Mohit is older than Kunal but younger than Sandeep.
(II) Tarun is younger than Sandeep but older than Mohit. Below is given a pair of questions, which are required to be answered, and a triad of statements. Which group of statements is sufficient to answer both the questions?
Question 1: Who is sitting opposite to Q?
Question 2: Who is sitting to the right of Q?
Statement 1 : P and U are sitting on left and right sides of T, respectively
Statement 2: P, Q, R, S, T and U are sitting around a round table with six chairs
Statement 3: Q is NOT sitting on the immediate left side of R
- Area of a rectangle with length x and breadth y is P and area of a parallelogram (which is strictly not a rectangle) with adjacent sides of length x and y is Q.
Question : Is \(P > Q\)?
Statement-I: \(x : y = 2 : 1\)
Statement-II: The angle between the two adjacent sides of the parallelogram is \(60^\circ\). - A circle touches all the four sides AB, BC, CD, DA of a quadrilateral ABCD.
Question : What is the perimeter of the quadrilateral?
Statement-I: \(AB + DC = 10\) cm
Statement-II: \(AD + BC = 10\) cm
