atalpanditgmat wrote:
Zarrolou wrote:
Actually I have found a QUICK way, check this out.
the first 8 can be written as:
\(x , x+2,...,x+14\)
the second 8 can be written as
\(x+16,x+18,...,x+30\)
As you notice, there is a gap of 16 between each number and its corrispondent 8 positions after 1st=x 9th=x+16
So if we add the sum of the gaps 16*8 to the sum of the numbers without the gap = 424 we have the result
16*8+424=552
Thnaks Zarrolou, I am still lost somewhere. Am i missing anything basic mathematics in your explanation. Please simplify further.
Hi atalpanditgmat, let me explain my method.
We have 16 numbers even and CONSECUTIVE so they can be expressed as: \(x, x+2, x+4, x+6, x+8, x+10, x+12, x+14, x+16, x+18, x+20, x+22, x+24, x+26, x+28, x+30\)
Here they are. Now look at this:
evrey number in the first 8, has a gap of 16 to its corrispondent 8 positions after. That's the trick.
ie: first is \(x\) => 9 pos after => \(x+16\)
second is \(x+2\) => 9 pos after =>\(x+2+16\)
So every number in the last 8 can be written as \(1st+16\), \(2nd+16\) and so on.
The sum of 1st 2nd 3rd 4th ... 8th is \(424\), so the sum of 9th 10th ... 16 th or (using the trick) \(1st+16, 2nd+16, 3rd+16, 4th+16, ... 8th+16\) is \(424\)(the sum of the numbers without 16)+\(16*8\)(the sum of 16s)
Let me know if it's clear now