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27 Oct 2019, 22:10
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:52) correct
27%
(01:54)
wrong
based on 66
sessions
History
Date
Time
Result
Not Attempted Yet
There are 28 students in a class. The first student draws a line of length ‘a’ units on the black board of the class. The second student draws a line of length ‘b’ units (a is not equal to b) on the black board of the class. The third student draws a line whose length is the average of the lengths of the two lines that are drawn by the first and second student on the black board. The fourth student draws a line whose length is the average of the lengths of the lines that are drawn by the first, second and third student. This process of drawing lines on the black board continues till the twenty-eighth student of the class. How many students drew the line having the same length?
A. 28
B. 27
C. 26
D. 25
E. 24
A. 28
B. 27
C. 26
D. 25
E. 24
27 Oct 2019, 22:45
Kudos
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The length drawn by 1st student is a, by 2nd student is b. Now by 3rd, we have the average of both the lines. (a+b)/2. Now for the 4th student, we have an average of all the 3 lines by 3 students. So {a+b+(a+b)/2}/3 = 3(a+b)/6 = (a+b)/2. For the 5th student, the line will be the average of all the 4 lines, i.e. {a+b+(a+b)/2+(a+b)/2}/4 = 2(a+b)/4 = (a+b)/2. So we are getting the average of the first two lines always from the 3rd student onwards. Therefore, out of 28 students, 26 of them drew the same line. So C is the correct choice.
