Problem Solving

There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 705. How many houses are there?

A. 61
B. 71
C. 81
D. 91
E. 101

* An answer will be posted in two days.

IMO 81

(705 - 545)/2 + 1 = 81

The number of consecutive odd numbers is (Last term-Frist term)/2+1. Then, (705-545)/2+1=81, and the correct answer is C.

Simple Solution to this

705 - 545 then divide by 2 + 1 = 81

We are interested only in the doorplates which have odd numbers, so we have to exclude the pair numbers.

Between the first doorplate "545" and the last doorplate "705" are (705-545) / 2 +1 odd numbers . i. e. we have 160 / 2 + 1 = 81.

We divided by 2 to separate the pair numbers to the odd numbers, and we add 1 at the end to include the last number because it is odd (705). If the last number would be 704 for example, we should not have to add the 1 at the end.

The correct answer is C.