Consecutive Integer Question

[milanproda]

Which of the following can be odd?

1- The sum of 7 consecutive numbers

2- The sum of 10 consecutive integers

3- The product of 13 consecutive integers

A- 2 ONLY
B- 1 AND 2 ONLY
C- 1 AND 3 ONLY
D- 2 AND 3 ONLY
E- 1, 2, AND 3

Would anyone happen to now the best way to solve this question without going through the long math?

[Tani]

1. Seven consecutive number can either be:
even + odd + even + odd + even + odd + even = which would be odd (try picking numbers - 2 thru 8)
or:
odd + even + odd + even + odd + even + odd = which would be even (try 1 thru 7)

2. sum of ten consecutive integers would be 5 even (total even) and 5 odd (total odd) whether starting with an odd or an even number. Therefore the grand total would be odd.

3. product of 13 consecutive integers must include either 6 or 7 multiples of two therefore it can only be even.

Therefore both 1 and 2 CAN BE odd.

no math needed!

[milanproda]

Tani, Thank you again! I have posted another consecutive integer problem on the forum, if you have a chance please help me out!