Odd and even

If a is equal to the sum of the odd integers from 15 to 35, inclusive, and b is the number of even integers from 15 to 35, inclusive, what is the value of a - b ?


There're 11 odd integers between 15 and 35 inclusive, and 10 even integers (B).

Sum of odd integers = n/2 [2a + (n-1) d] where n is the no. of terms, a is the 1st term, and d is the difference between the terms


A (sum of odd integers) = 11/2 [(2*15) + ((11-1) * 2)]

= 275


A- B = 275 - 10 = 265

Answer [spoiler]D = 265[/spoiler]

A similar explanation as MBA.Aspirants's, but number driven !

a = Sum of odd integers from 15 to 35 = 15 + (15+2)+ (15+4) .....(15+20) = 15 + 15 + 2 + 15 + 4 ...15 + 20 = (15*11)+(2+4+...20) = 165 + 2(1+2+...10) = 165 + 2(55) = 275 [Sum of first n integers = n*(n+1)/2]

b = # of even integers from 15 to 35 = n(16,18,20,22,24,26,28,30,32,34) = 10

a-b = [spoiler]275-10 = 265 [/spoiler]