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Q2 AVERAGES

A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35( 7/17 ). What was the number erased?

a. 7

b. 8

c. 9

d. None of these

A better and easier method is as follows:
First of all, when ever a number is deleted from consecutive numbers,
avg cant change more than 1/2.
So in this case new
avg is 35 7/17, so old average was 35.

  Now, 35 is avg of first 69 numbers, so previously there were 69 num, and now there are 68(after deletion).
Now, 7/17 = 28/68 . So effectively, the number which was deleted gave 28/68 to each 68
num left, so the number should have been 28 less than 35(old avg)
Ans= 35-28=7

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