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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?
11
12
10
13
11
Total people = (Left rank of Cherry) + (Right rank of Juno) - Total people in row + People between them. Rearranging gives: People between = (Position from left of Cherry + Position from right of Juno) - Total people - 2.
Total people = (Left rank of Cherry) + (Right rank of Juno) - Total people in row + People between them. Rearranging gives: People between = (Position from left of Cherry + Position from right of Juno) - Total people - 2.
Analyze Given Data
Total number of people in the row is 41. Cherry is 31st from the left end, and Juno is 23rd from the right end.
Check for Overlapping
Add Cherry's left rank (31) and Juno's right rank (23), which gives 31 + 23 = 54. Since 54 is greater than the total number of people (41), the positions overlap.
Apply Formula for Overlapping Arrangement
Number of people between two persons = (Sum of ranks from both ends) - Total people - 2. Substituting the values: (31 + 23) - 41 - 2 = 54 - 43 = 11.
B: 12 is incorrect because the calculated difference requires subtracting 2 for the two overlapping persons, yielding 11. C: 10 is incorrect due to arithmetic error in subtraction. D: 13 is incorrect and overestimates the intermediate count.
A is correct because the number of people between Juno and Cherry in an overlapping ranking row is calculated as (31 + 23) - 41 - 2 = 11.
Always check whether the sum of positions from opposite ends exceeds the total strength. If Sum > Total, use the overlap formula: (Rank 1 + Rank 2) - Total - 2.