Problem Solving

What is the sum of all the two-digit
positive integers whose two digits are
odd?
(A) 1225
(B) 1275
(C) 1325
(D) 1375
(E) 1425

here's my take ...
sum of 11, 13, ...,19 = no of terms * avg
no of terms = 5
avg = 15
sum = 75

note that sum of 31, 33.... each term is 20 more than prev series so add 20 * 5 to prev addition = 75 + 100
next series each term is 40 more... add 200 to 75
next series 60 more, add 300 to 75
next series 80 more, add 400 to 75

total sum = 75 +175 + 275 + 375 + 475 = 1375

ans choice D

hope this helps...

Shorter approach:

The set of two-digit numbers with odd digits has some nice symmetry:

11, 13, ...
31, 33, ...
51, 53, ...
71, 73, ...
91, 93, ...

There are 5 numbers in each row, and there are 5 rows, so there are 25 numbers.
Since the numbers in each row have an average of 15/35/55/75/95, the average of ALL of the numbers is 55 (it is in the middle of that list of evenly spaced numbers).

So, 25*55=?