UIL2012C

[smeag]

please provide explanations for questions:

31, 37, 41,43, 47,54, 56

[nsguy1350]

Alright, I took it just now, so I can answer your questions. Unfortunately, I had already seen the test before :( and I still got a 312, doing all 60 and missing 6 (OK, actually a 306, I wasin the process of marking down my answer as time hit 0:00).

31. 4C2 x 10C7 x 5C3.

37. Just add up the bases. However, you will notice that adding that each of those is one of the next place (as in 99 is one off 100 for base 10, 66 is one off from 100 in base 7, 55 is the same for 100 in base 6, etc.). Therefore, you can just add [unparseable or potentially dangerous latex formula] to get a total of 157.
41. 3 + 4 + 6 + 8 + 10 + ....
I went to 3+4 in my calculator, and said the place "2". Then, I counted on, as I added 4,6,8,... I could've started farther in the sequence, or used my NS skills, but I didn't want to risk a mistake.

43. I got this one wrong, I thought it was 5P2, Actually, I think I remember hearing this one was an answer key mistake, and it should be D.20.

47. Apparently I got this one wrong, but you can trig your way through it. Remember that bearing means you add 90 degrees to the angle.

54. I got this one wrong, because the LCM of 3 and 5 is not 8. I forgot this trick, and I would've put 5, which is correct, but I need to look at another post to make sure I can tell you correctly. I'll see if I can find it and give you the link. The problem is that when you divide 80 and 15, you don't get an integer answer, which trips me up.

56. I got this one wrong as well. I put 32 instead of 16. I figured out you can add the "not" numbers and then divide by the number of hair colors minus one (2 here), but now I have forgotten why. My in-test proof gave me 32, so I can't really help with this one because I'm not sure what I did wrong.

I am rusty on this test :'(

EDIT: typo fixed, 157, not 133 on 41.
EDIT2: Another typo fixed, I'm a failure.

[redhawk2015]

#41: The differences between the numbers are 4, 6, 8, 10...some quick brute-force addition shows the answer to be [unparseable or potentially dangerous latex formula]

#43: Not sure about this one. The answer it says is correct is [unparseable or potentially dangerous latex formula], but I don't really see how. Anyone else have an idea?

#54: The solution with the highest possible [unparseable or potentially dangerous latex formula] is [unparseable or potentially dangerous latex formula]; from there, keep taking away 3 y's and adding 5 x's. The list of solutions is [unparseable or potentially dangerous latex formula]. This is a total of [unparseable or potentially dangerous latex formula] solutions.

#56: Set [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]. Then [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula], and [unparseable or potentially dangerous latex formula]. Add all these equations together to get [unparseable or potentially dangerous latex formula]. Divide by 2 to get [unparseable or potentially dangerous latex formula]

[nsguy1350]

By the way, the answer key and I both say 54 is not 6, but 5. That's the brute force way, but there are faster solutions.
Positive integers, no (0,16) won't work.

[redhawk2015]

Oh. Oops.