Class Rank Calculation: Finding Total Students
Problem Analysis
The question asks us to determine the total number of students in a class. We are given Ariel's position in the class ranking from two different perspectives: her rank from the top and her rank from the bottom.
- Ariel's rank from the top is \(6^{th}\).
- Ariel's rank from the bottom is \(18^{th}\).
To find the total number of students, we need to consider Ariel's position and the students above and below her.
Solution Steps
There are two common ways to solve this type of ranking problem:
Method 1: Counting Students Above and Below
1. Identify students above Ariel: Since Ariel is \(6^{th}\) from the top, there are \(6 - 1 = 5\) students ranked above her.
2. Identify students below Ariel: Since Ariel is \(18^{th}\) from the bottom, there are \(18 - 1 = 17\) students ranked below her.
3. Calculate the total: The total number of students is the sum of students above Ariel, Ariel herself, and the students below Ariel.
The formula is: \( \text{Total Students} = (\text{Students above Ariel}) + (\text{Ariel}) + (\text{Students below Ariel}) \) Substituting the values: \( \text{Total Students} = 5 + 1 + 17 \) \( \text{Total Students} = 23 \)
Method 2: Using the Rank Formula
1. Understand the formula: When calculating the total number of items in a single list based on rank from both ends, we add the rank from the top and the rank from the bottom. However, since the item itself (Ariel, in this case) is counted in both ranks, we must subtract 1 to avoid double-counting.
2. Apply the formula: \( \text{Total Students} = (\text{Rank from Top}) + (\text{Rank from Bottom}) - 1 \) Substituting Ariel's ranks: \( \text{Total Students} = 6 + 18 - 1 \) \( \text{Total Students} = 24 - 1 \) \( \text{Total Students} = 23 \)
Conclusion
Both methods confirm that there are 23 students in the class. Ariel's position is accounted for exactly once in the total count.
Similar Questions
In a row of 34 students facing North, Jignesh is 12th from the right end. If Kamlesh is 7th to the left of Jignesh, what is Kamlesh's position from the left end of the line?
All 41 people are standing in a row, facing north. Juno is 23rd from the right end, while Cherry is 31st from the left end. How many people are there between Juno and Cherry?
X’s rank was 12 from the top. If the total number of students in the class was 16, then X’s rank from the bottom for the class is:
Each of Preeti, Kiran, Grace, Ankit, Deepak, Nitin and Neelam has an exam on a different day of a week, starting from Monday and ending on Sunday of the same week. Preeti has an exam on Thursday. Only one person has an exam between Preeti and Nitin. Grace has exam on the day immediately before Nitin but not on a Monday. Only two people have exams between Grace and Deepak. Neelam’s exam is on one of the days before Ankit’s but on one of the days after Kiran’s. Who among the following has an exam on Monday?
Student are sitting in a row in which the position of X is 17 th from the left and that of Y is 14 th from the right. If they interchange their positions, X’s position becomes 7 th from the left. How many students are there in the row?
All 36 students in a class are standing in a row facing north. Preeti is 12th from the right end while Alisha is 22nd from the left end. How many people stand between Preeti and Alisha?
In a row of people, all facing north, Bunty is 8th from the left end. Sneha is 15th from the left end. Sneha is exactly between Bunty and Nupur. If Nupur is 7th from the right end of the line, how many people are there in the row?
Anju ranked 18th from the bottom and 15th from the top in his class. How many students are there in his class?
A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. D lives on an odd-numbered floor but not 3. The sum of floors on which D and E live is 7. A lives immediately below C. F lives on the top floor. How many people live between E and F?
If 'A' stands for '÷', 'B' stands for 'x', 'C' stands for '+' and 'D' stands for '-', what will come in place of the question mark '?' in the following equation?
34D54C18A18B324 = ?
Important Questions from Ordering and Ranking
- Each of the digits in the number 8731245 is arranged in ascending order from left to right. The position(s) of how many digits will remain unchanged as compared to that in the original number?
- Varun ranked 34th from the top and 11th from the bottom in his class. How many students are there in his class?
- Piyush ranked 35th from the top and 18th from the bottom in his class. How many students are there in his class?
- Each of the digits in the number 81674293 is arranged in ascending order from left to right. Which of the following digits will be fourth from the left?
- Mr. Into ranked 96th from the top and 31st from the bottom in his class. How many students are there in his class?
