Ifaequals the sum of the even integers from 2 to 120, inclusive, andbequals the sum of the odd ...
Ifaequals the sum of the even integers from 2 to 120, inclusive, andbequals the sum of the odd integers from 1 to 119, inclusive, what is the value of a - b ?
Answer/Solution
60
Steps/Work
This is a solution from Beatthegmat:
even numbers:
(120-2)/2 + 1 = 60 even integers.
(120+2)/2 = 61 is the average of the even set.
sum = avg*(#of elements) = 61*60 =3660 = a
odd numbers:
(119-1)/2 + 1 = 60 odd integers.
(119+1)/2 = 60 is the average of the odd set.
sum = avg*(#of elements) = 60*60 = 3600 = b
a-b = 3660 - 3600 = 60. Answer : A
even numbers:
(120-2)/2 + 1 = 60 even integers.
(120+2)/2 = 61 is the average of the even set.
sum = avg*(#of elements) = 61*60 =3660 = a
odd numbers:
(119-1)/2 + 1 = 60 odd integers.
(119+1)/2 = 60 is the average of the odd set.
sum = avg*(#of elements) = 60*60 = 3600 = b
a-b = 3660 - 3600 = 60. Answer : A