Among the five poles—I, N, C, H, and L—each having a different height, which pole is the shortest?
(I) C is taller than only two poles. I is shorter than C and N is shorter than I.
(II) H is taller than L.
Pole Height Comparison: Statement Analysis
The objective is to determine the shortest pole among five poles (I, N, C, H, L), given that each has a distinct height. We must evaluate the sufficiency of the provided statements.
Evaluating Statement I
- Statement I provides two key pieces of information:
- Firstly, "C is taller than only two poles." This implies C is the third tallest pole out of the five. If we denote the heights in descending order (tallest to shortest), C occupies the 3rd position. The two poles shorter than C are in the 4th and 5th positions.
- Secondly, "I is shorter than C and N is shorter than I." This establishes a relative height order: \(N < I < C\).
- Combining these facts: Since C is taller than exactly two poles, and we know from the second part of the statement that N and I are shorter than C (\(N < I < C\)), it follows that N and I must be those two poles.
- Therefore, the height order from tallest to shortest must be: \((Pole\;A) > (Pole\;B) > C > I > N\), where Pole A and Pole B are the remaining poles (H and L).
- This arrangement definitively identifies N as the shortest pole.
Statement I alone is sufficient to answer the question.
Evaluating Statement II
- Statement II states: "H is taller than L."
- This translates to the inequality \(H > L\).
- This statement only provides the relative height between H and L. It does not relate H or L to C, I, or N, nor does it provide enough information to determine the shortest pole among all five.
Statement II alone is not sufficient to answer the question.
Final Conclusion on Sufficiency
Since Statement I alone provides sufficient data to conclusively determine the shortest pole (N), while Statement II alone does not, the data in Statement I alone is sufficient.
Similar Questions
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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?
