Consider the following question and decide whether any of the statements among the given statements are adequate to answer that question. What is the total number of students in the class? Statements: 1. Mr X’s rank was 15 th from the top in the class. 2. Mr X’s rank was 26 th from the bottom of the class.
Both 1 and 2 together are sufficient to answer the question.
Data Sufficiency Analysis: Finding Total Students from Rank
This question asks for the total number of students in a class. We are given two statements about Mr. X's rank, and we need to determine if either statement alone or both statements together are sufficient to answer the question.
Analysing Statement 1: Mr. X's rank from the top
Statement 1 says: Mr X’s rank was 15th from the top in the class.
This statement tells us there are 14 students ranked above Mr. X. However, it gives no information about the number of students ranked below Mr. X. Without knowing the number of students below him, we cannot determine the total number of students in the class.
Therefore, Statement 1 alone is not sufficient to answer the question about the total number of students.
Analysing Statement 2: Mr. X's rank from the bottom
Statement 2 says: Mr X’s rank was 26th from the bottom of the class.
This statement tells us there are 25 students ranked below Mr. X. However, it gives no information about the number of students ranked above Mr. X. Without knowing the number of students above him, we cannot determine the total number of students in the class.
Therefore, Statement 2 alone is not sufficient to answer the question about the total number of students.
Analysing Statements 1 and 2 Together
Now, let's consider both statements together:
- Statement 1: Mr. X's rank from the top is 15th.
- Statement 2: Mr. X's rank from the bottom is 26th.
If we know a person's rank from both the top and the bottom in a linear arrangement (like ranks in a class), we can find the total number of people. The formula to calculate the total number of students is:
Total students = (Rank from Top) + (Rank from Bottom) - 1
We subtract 1 because Mr. X is counted twice, once when calculating the rank from the top and once when calculating the rank from the bottom.
Using the information from both statements:
Rank from Top = 15
Rank from Bottom = 26
Total students = $15 + 26 - 1$
Total students = $41 - 1$
Total students = $40$
With both statements combined, we can definitively determine the total number of students in the class is 40.
Therefore, both statements 1 and 2 together are sufficient to answer the question.
Conclusion on Data Sufficiency for Total Students
Based on our analysis, neither Statement 1 alone nor Statement 2 alone is sufficient. However, both statements together provide enough information to calculate the total number of students in the class.
The question asks which statements are adequate to answer the question. Our analysis shows that only the combination of Statement 1 and Statement 2 is sufficient.
Thus, the correct choice is the one indicating that both statements together are sufficient.
Revision Table: Total Students Data Sufficiency
| Statement(s) Considered | Sufficient to Answer? | Reasoning |
|---|---|---|
| Statement 1 Alone | No | Gives rank from top, but not bottom. Number of students below is unknown. |
| Statement 2 Alone | No | Gives rank from bottom, but not top. Number of students above is unknown. |
| Statements 1 and 2 Together | Yes | Provides rank from both top and bottom. Total students can be calculated using the formula: Top Rank + Bottom Rank - 1. |
Additional Information: Rank and Total Calculation
Problems involving ranks are common in logical reasoning and quantitative aptitude sections. Understanding the relationship between a person's rank from different ends of a sequence and the total number of items in that sequence is crucial.
Key points to remember:
- If a person's rank from the top is 'T' and their rank from the bottom is 'B' in a line or list, the total number of people (N) is given by the formula: $N = T + B - 1$.
- The '-1' is essential because the person whose rank is given is counted in both the top count and the bottom count.
- Conversely, if you know the total number of people (N) and a person's rank from one end (say, rank from top 'T'), you can find their rank from the other end (rank from bottom 'B') using a rearrangement of the formula: $B = N - T + 1$. Similarly, $T = N - B + 1$.
- Data sufficiency problems require you to check if the given statement(s) provide enough information to find a unique answer to the question, not necessarily to find the answer itself (though calculating it helps confirm sufficiency).
In this problem, knowing both ranks allowed us to find the total number of students (40), confirming that the combined information is sufficient.
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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?
