Number properties guide, Chapter 4 Q 10

by **Guest** Wed Apr 16, 2008 7:44 pm

Is the sum of integers from 54 to 153, inclusive divisible by 100?

The answer says NO, by saying the sum of n consecutive numbers is not divisble by n if n is even

Here is what I am doing

Sum of consecutive integers between X and Y, inclusive (X < Y) is

(X+Y)/2 * [(Y-X)+1)]

(54+153)2 * (100)

That is divisible by 100.

Where I am screwing up?

by **Tanuj** Thu Apr 17, 2008 8:18 pm

The problem is (y+x) is not divisible by 2

i.e. (153+54)/2 is not an integer.

by **Guest** Fri Apr 18, 2008 9:18 am

Ron/Stacey

??

by **StaceyKoprince** Mon Apr 21, 2008 6:34 pm

Tanuj has got it.

Just because you multiply some number by 100 does not make it divisibly by 100. I can multiple 4.93 by 100 to get 493. But if I divide 493 by 100, the result is not an integer.

Keep going with your numbers. 153+54 = 207. 207/2 = 103.5. 103.5*100 = 10350, the sum. 10350/100 = 103.5, which is not an integer. So the sum, 10350, is not divisible by 100.