x = sum of even Integers

[ndcruz]

If x is equal to the sum of the even integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusinve, what is the value of x+y?

 

(A) 550

(B) 551

© 560

(D) 561

(E) 572

 

 

OA: D

 

[krovvidy]

There would be 11 even integers from 40 to 60 ....

 

As these are consecutive, we can say that SUM of those is (40+60/2) *11 = 550.

 

So, the final answer is 550+11 = 561 (D)

[Dynamo]

D 561

[ve_boss]

Sorry about this question, but I like to be convince by formula. (my french side I guess..) : can someone explain this step :

 

As these are consecutive, we can say that SUM of those is (40+60/2) *11 = 550

 

It reminds me smth but I don't manage to demonstrate this formula again.

 

Thanks !

[ve_boss]

ok. I just remembered that

sum(1,n) = n*(n+1)/2, which is a particular arithmetic serie.

 

But I forgot that

http://upload.wikimedia.org/math/9/a/5/9a5fb55b3d24acaa271a9e4eea85cd83.png

 

:blush:

[Dynamo]

Sn= {n+1(first term + Last term)}/2

 

AP .....

[Dynamo]

ok. I just remembered that

sum(1,n) = n*(n+1)/2, which is a particular arithmetic serie.

 

But I forgot that

http://upload.wikimedia.org/math/9/a/5/9a5fb55b3d24acaa271a9e4eea85cd83.png

 

:blush:

 

n(n+1)/2

 

is only for a series of HP

 

1+2+3+4+5...... +n....