Sums of Evenly Spaced Sets

[von]

Is the sum of the integers from 54 to 153, inclusive, divisible by 100? I answered Yes, but the MGMAT claims the answer is No.

My Rationale:

1. Sum = Avg*(Num_of_items)
2. Avg = (First+Last)/2 = (54+153)/2 = 103.5
3. Num_of_items = (Last-First)+1 = (153-54)+1 = 100
4. Thus, Sum = 103.5*100 = 10,350
5. 10,350/100 = 103.5; thus, the sum of the integers from 54 to 153 inclusive IS divisible by 100.

Wait, I just noticed something, wow, I feel stupid. Never mind.

Epiphany: Just because you can divide one integer X by another integer Y, and receive a number Z (integer or non_integer) does NOT mean X is divisible by Y! In order for X to be divisible by Y, Z MUST be an integer, if Z is a non_integer, then X is NOT divisible by Y. So in my example, 103.5 was my Z and I see the problem and solution now. Thanks, v

[edvhou812]

The terms all sum up to 10,350, so it looks like the answer would be "yes" since there is a zero at the end, but once we try to divide 10350/100 it doesn't work out.