If S is the sum of integers from 30 to 50, inclusive, how many different prime factors does S have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Oa is D
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Oa is D
To know the prime factors, it is better to get the number, so the core of the problem is to calculate S, the sum of integers from 30 to 50
I use the formula
"the sum for i=0 to n" of i= n(n+1)/2
A="the sum for i=0 to 50" of i = 50*51/2=1275
B="the sum for i=0 to 29" of i = 29*30/2=435
Now to get S we need to do add A and subtract all the members we do not want, namely B
S=A-B=1275-435=840
Now, it's ok
840=2.2.2.3.5.7
There are 4 different prime factors.
