Inv. A 2011

[FabensMath]

I got a 286. These are the one i either got wrong or i just didn't know how to do. Can you help me? Thanks

20. the directrix of the conic given by the equation [unparseable or potentially dangerous latex formula](i'm rusty on conics, i can't remember)

31. A set of 5 integers has a mean of 7, a mode of 6, and a median of 6. What is the smallest possible range of the set of integers?(Is there a trick to this)

36. Three letters are randomly chosen from the word EIGHT. What are the odds that the set of three letters randomly chosen consist of at least 2 consonants?

37. The Yu Knee Cu tribe uses a different base other than base 10 to solve their math problems. Using their base they calculated that 34+43=121 and 43-34=5. What answer should they get for 33x4?

54. The Sweet Tooth candy store has four different types of gum balls, a sweet ball, a sour ball, a hot ball, and a red hot ball. They package them in sets of three. How many ways can the store package the gum balls?

[nsguy1350]

20. Put it in standard form [unparseable or potentially dangerous latex formula], then find the directrix by using [unparseable or potentially dangerous latex formula]. k+p applies when you have a parabola pointing down.

31. Not sure, I've seen this a couple times and have no idea how to do it.

36. I just wrote out all 10 combinations, then found that 7 work, for 7/3 odds.

37. [unparseable or potentially dangerous latex formula]. That gives a, the base.
[unparseable or potentially dangerous latex formula]. Obviously you know that the base isn't -1, so you have base 6. 33 x 4 base 6 = 220, I believe.

54. This is not am easy 4C3 problem because you're basically picking from a set that has more than one of each type of gumball. For example, in 4C3 rules, you couldn't pick a sweet, sweet, sweet, and then sour, while here, you can. Thus, you do [unparseable or potentially dangerous latex formula].

[PokémonMaster]

What I would do for #31 put in 3 sixes to begin with. This satisfies the mode, the median, and because it is the highest possible bottom number.Then take the total (35) minus what you currently have (18) and take the two integers closest to each other that add up to this. This satisfies the mean and gives you the answer(if the answer was 3). If this does not give the correct answer then I have no idea.

[FabensMath]

Yes, the answer was 3, and thanks! both of you!
I'm gonna be taking invitational B'11 and i'll post questions later.