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
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Important Questions from Ordering and Ranking
Three persons A, Band Care standing in a queue not necessarily in the same order. There are 4 persons between Aand B, and 7 persons between Band C. If there are 11 persons ahead of Cand 13 behind A, what could be the minimum number of persons in the queue?
In a class of 60 students, where the number of girls is twice that of boys, Kamal, a boy, ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is:
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled on Monday?
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled between Statistics and English?
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is the last one in the week?
