FelixM wrote:
The way I did it took me a long time (4 min), so I would welcome some quicker way or some rules/theory regarding this problem.
I tested out all the answer choices against 3 sets of consecutive integers, to see which set will be even each time:
1,2,3,4,5 / 2,4,6,8,10 (all even) / 1,3,5,7,9 (all odd) and got the following results:
a) Even/Even/Odd
b) Odd/Even/Even
c)Even/Even/Odd
d)Odd/Even/Even
e) Even/Even/Even. Only Choice E using the 3 sets could always produce an even result, so E was the answer.
Is there a faster way, or should I have know the general notation of an odd integer vs an even integer?
Thanks!
It looks like you chose the wrong number sets. Since we are dealing with consecutive numbers, {1, 2, 3, 4, 5} and {2, 3, 4, 5, 6} would have been good. Even better, since this question rests on even/odd and our consecutive 5 numbers will alternate between even and odd, you can save a few seconds by using {odd, even, odd, even, odd} and {even, odd, even, odd, even}.
From here, you can then jot down one of those even + even = even, even + odd = odd, etc... tables.
Going through the options one by one using this setup:
A) a + b + c -> e + e + e OR o + o + o. e + e + e will always be even. o + o + o becomes e + o, which results in an odd.
B) ab + c -> The product of two consecutive numbers will always be even. We have e + e and e + o. e + o results in an odd.
C) ab + d -> e + o and e + e. e + o is odd.
D) ac + d -> (e * e) + o or (o * o) + e. These become e + o and o + e. Both are odd.
E) ac + e -> (e * e) + e or (o * o) + o. These become e + e and o + o. Both are even.
Because E is the only option that gives us all evens, E must be the correct answer.