Difficulty: Easy
Correct Answer: 46
Explanation:
Introduction / Context:
This ranking question requires you to use both the rank from the top and the rank from the bottom of a class to determine the total number of students. This type of problem appears regularly in reasoning tests, and the relationship between these ranks is a standard concept you should know.
Given Data / Assumptions:
Concept / Approach:
For a person in a line, the sum of their rank from the top and their rank from the bottom is always equal to the total number of persons plus 1. This is because if you move from the top to the person and then continue to the bottom, you count every person exactly once, plus the counted position of that person.
Step-by-Step Solution:
Step 1: Let the total number of students be N.Step 2: Use the relation: rank from top + rank from bottom = N + 1.Step 3: Substitute Sam's ranks: 9 + 38 = N + 1.Step 4: Compute 9 + 38 = 47.Step 5: So 47 = N + 1, which gives N = 47 - 1 = 46.Step 6: Therefore, there are 46 students in the class.
Verification / Alternative check:
We can verify by checking: N + 1 should equal 46 + 1 = 47. Sam's ranks are 9 from the top and 38 from the bottom, and 9 + 38 does indeed equal 47, confirming that our calculation is consistent with the standard rule.
Why Other Options Are Wrong:
If N were 45, then N + 1 would be 46, which does not match the sum of 9 and 38. Similarly, 47 and 48 would give N + 1 values that fail to equal 47. Only N = 46 correctly satisfies the fundamental relationship between top and bottom ranks for the same student.
Common Pitfalls:
Sometimes students mistakenly add the ranks and forget to subtract 1, which would give 47 instead of 46. Others may try to average the ranks, which has no relevance here. Remember the key formula rank from top + rank from bottom = total + 1 and apply it directly.
Final Answer:
The total number of students in the class is 46.
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