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.
The question asks to identify the shortest person among Harsh, Ketan, Mayank, Rohit, and Sidharth using two statements about their heights.
Statement I Analysis
Statement (I) provides the following information:
- Mayank is taller than Harsh: $Mayank > Harsh$
- Mayank is shorter than Ketan: $Ketan > Mayank$
Combining these, we get the order: $Ketan > Mayank > Harsh$. This tells us Harsh is shorter than Ketan and Mayank. However, the heights of Rohit and Sidharth are unknown relative to this group. Therefore, Statement I alone is not sufficient.
Statement II Analysis
Statement (II) provides the following information:
- Rohit is taller than Harsh: $Rohit > Harsh$
- Rohit is shorter than Mayank: $Mayank > Rohit$
Combining these, we get the order: $Mayank > Rohit > Harsh$. This tells us Harsh is shorter than Mayank and Rohit. However, the heights of Ketan and Sidharth are unknown relative to this group. Therefore, Statement II alone is not sufficient.
Combined Statements Analysis
Combining the information from both statements:
- From Statement I: $Ketan > Mayank > Harsh$
- From Statement II: $Mayank > Rohit > Harsh$
Putting them together, we can establish the following partial order:
$Ketan > Mayank > Rohit > Harsh$
This combined information shows that Harsh is shorter than Ketan, Mayank, and Rohit. However, the position of Sidharth is not mentioned in either statement. Sidharth could be shorter than Harsh, making Sidharth the shortest, or Sidharth could be taller than Ketan, or anywhere in between. Since Sidharth's height is unknown, we cannot definitively determine who is the shortest person.
Conclusion
Both statements, when combined, are insufficient to answer the question because the height of Sidharth is unknown.
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. 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. - 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.
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. 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
