Discussion
Suresh ranked 23rd from the top and 23rd from the bottom in his class. How many students are there in the class?
Answer: C
There are 45 students in the class.
Suresh has 22 students above him and 22 below him. Counting Suresh himself, the class has 22 + 22 + 1 = 45 students, that is 23 + 23 − 1.
46 forgets that Suresh is counted in both ranks. 47 and 50 do not come out of the counting.
Draw the class as a line: 22 students stand above Suresh, then Suresh, then 22 below. The count is 22 + 1 + 22 = 45. Whenever the rank from the top equals the rank from the bottom, the total is 2n − 1, which gives 45 here.
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