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Averages

by Vincen » Mon Oct 23, 2017 6:45 pm
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

The OA is C.

Wow, I think this is a really hard question. Experts, may you tell me what is the best way to solve it? Thanks.
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by GMATGuruNY » Mon Oct 23, 2017 7:48 pm
Vincen wrote: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
Let the first line = 2 inches and the second line = 4 inches.
Third line = average of the two preceding lines = (2+4)/2 = 3 inches.
Fourth line = average of the three preceding lines = (2+4+3)/3 = 3 inches.
Fifth line = average of the four preceding lines = (2+4+3+3)/4 = 3 inches.
Notice the PATTERN.
After the first two lines, all of the subsequent lines have THE SAME LENGTH (3 inches).
Implication:
After the first two lines, the remaining 26 lines will all have the same length.

The correct answer is C.
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