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