So, just as I was going to bed last night, it dawned on me that my 10-second solution "theory" is incorrect.
That said, here's the general idea (of my flawed theory) ...
Step 1. We COULD determine the total number of games (45), which means we COULD calculate the total number of points to be awarded (90 points in total, since 2 points are awarded with each game).
Step 2. We COULD determine the total number of points awarded to teams A, B, C, D, E, F, G, H and I.
Step 3. Whatever points are unaccounted for would be the number of points that Team J must have received.
For example: If, in step 2 we found that a total of 85 points were awarded, then we'd know that there are 5 unaccounted points, which means Team J must have received those 5 points.
So far, this is similar to pushpitkc's solution. However, we may not need to perform any of the above calculations. Here's why.
If it turned out that Team J must have received 5 points (as in the above example), then we'd be hard pressed to determine Team J's record, since there's more than 1 way for a team to receive 5 points.
For example, Team J could have won 0 games, tied 5 games and lost 4 games
Or Team J could have won 1 game, tied 3 games and lost 5 games
Or Team K could have won 2 games, tied 1 game and lost 6 games
As you can see, each possibility yields a different answer to the question.
Since there can be only one correct answer to the question, my reasoning was that there must be exactly 1 point that's unaccounted for. Consider these cases:
CASE A: If there were 0 points unaccounted for, then that would mean Team J lost all 9 of its games. HOWEVER, 9 is not among the answer choices. So, the answer choices tells us that CASE A cannot occur.
CASE B: If there was 1 point unaccounted for, then that would mean Team J tied 1 game and lost 8 games (answer E).
At this point, I incorrectly concluded that, if there is more than 1 point unaccounted for, then there will be more than 1 possible outcome (as is the above case, when we had 5 points unaccounted for)
This conclusion is wrong. To see why, check out case C below.
CASE C: If there were 2 points unaccounted for, then COULD would mean Team J won 1 game, and lost 8 games (answer E) OR it COULD would mean Team J won 0 games, tied 2 games and lost 7 games (but 7 is not among the answer choices)
So, if there were 2 points unaccounted for, the correct answer would have to be E.
CASE D: If there were 3 points unaccounted for, then COULD would mean Team J won 1 game, tied 1 game and lost 7 games (but 7 is not among the answer choices) OR it COULD would mean Team J won 0 games, tied 3 games and lost 6 games (answer D)
So, if there were 3 points unaccounted for, the correct answer would have to be D.
And so on.
I hope my "10-second" solution didn't drive some people crazy!
Cheers,
Brent
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