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Rajdeep ranked 64 th from the top and 23 rd from the bottom in his class. How many students are there in his class?
87
84
86
85
86
To calculate the total number of individuals in a linear sequence when a position is given from both ends, use the formula: Total = (Rank from Top + Rank from Bottom) - 1. Substituting the values 64 and 23 results in 87 minus 1, which equals 86.
To calculate the total number of individuals in a linear sequence when a position is given from both ends, use the formula: Total = (Rank from Top + Rank from Bottom) - 1. Substituting the values 64 and 23 results in 87 minus 1, which equals 86.
This logical principle of 'inclusion-exclusion' is foundational to set theory in mathematics, which is applied in the Census of India (Ministry of Home Affairs) to ensure that individuals are counted exactly once while accounting for overlapping data sets.
The 'minus 1' factor is necessary because the individual is counted twiceтАФonce in the top-down count and once in the bottom-up count.
This logic is frequently tested in Reasoning and General Intelligence sections of SSC CGL, CHSL, and IBPS examinations.
The total number of unique elements in two overlapping sets is calculated by the formula n(A union B) = n(A) + n(B) - n(A intersection B).
The formula Total = (L + R - 1) is a standard method used to determine the size of a row or class in aptitude testing.
Option A (87) is a common distractor for candidates who forget to subtract the duplicate count of the person.
Option B (84) and D (85) are incorrect calculations derived from failing to apply the rank-sum rule accurately.
C is correct тАФ The total number of students is determined by adding the two ranks and subtracting one to correct for the double-counting of Rajdeep.
When solving ranking problems, always verify if the person mentioned is the same in both ranks; if they are different individuals, the formula changes significantly.
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