FOF Highlander 5/16: Today's Quick Math Game

[wbatl1]

I’m going to continue QuikSand’s tradition of a random math game, since I won yesterday. Now, I’ll make it clear that I am a history guy, so there is not any cool or new math in this random math game, but I’ll ask you to harken back to the glory days, and the SAT. As you know, there are 5 answer choices on each question. A student who doesn’t care plans to take the SAT and “Dial down the Center,” and put C as the answer to every question. Now remember, in the SAT a ¼ point is deducted for every wrong answer. Your job is to guess the student’s RAW score, or the total (questions right)-(¼*questions wrong). The hypothetical exam section will have 80 questions, and as I said, the student will answer C (or the third answer choice) for every question. I will use a random number generator to create the “answer key,” and then use it calculate the RAW score. Whoever’s RAW score guess is the closest will win, and get to put on this game tomorrow or sometime soon. Hint: Do the simple math to find the appropriate range, and then all that comes into play is your luck. Enjoy!

If any clarification is needed, just ask!
If there is a tie, I will continue Quik’s tradition and will randomly pick a winner.

Since I am posting this a little later, I will probably run the game around 6:00, so that’s when entries are due.

So, send me your guess for the RAW score via PM

Good Luck!

[BrianD]

I be in.

[Chas in Cinti]

ok... dumb question, but should we be giving you the "SAT" answer (i.e. based on 800 perfect score), or strictly with how you explained (80 being perfect score)?

[KevinNU7]

ok... dumb question, but should we be giving you the "SAT" answer (i.e. based on 800 perfect score), or strictly with how you explained (80 being perfect score)?I think the best score would be 80 because he didn't give us a base score to start with, therefore the b ase is zero.

[wbatl1]

ok... dumb question, but should we be giving you the "SAT" answer (i.e. based on 800 perfect score), or strictly with how you explained (80 being perfect score)?

Yes, best possible score would be 80. The SAT takes the raw score and uses a curve to find the score out of 800, but all we're looking for is the RAW score. It's not a dumb question, I know I didn't explain it well.

[wbatl1]

Quick Last Minute Bump...

[wbatl1]

Last 10 Minutes...

[wbatl1]

OK, here is the math to find the mathematically correct answer. Since there is a 20% chance that C is right, we calculate that the student will get 16 questions right by multiplying 1/5*80. Then, the remaining 64 questions are wrong, which leads to a deduction of 16 points (64*1/4). So, the “correct” guess would be a 0 RAW score. This, incidentally, is the reason behind the encouragement to guess if you can eliminate one answer choice on the test. So, the perfect answer would have been 0. The range of answers I received was from 40 to –15. Incidentally, only 2 people guessed the “correct” answer 0. Also, only 4 out of the 13 answers I received were negative, even though the fulcrum should have been 0.

The “answer key” to the hypothetical test is below, with 1 representing A, 2 representing B, and so on. The C’s are bolded.

4 2 5 4 3 2 2 2
2 3 4 3 4 4 5 3
5 4 2 1 1 3 5 4
5 1 4 5 3 5 4 3
4 5 2 1 4 3 5 3
4 5 2 3 1 5 1 4
2 3 4 1 1 2 2 4
3 3 1 3 4 1 2 4
3 3 3 5 4 4 3 3
2 5 3 3 2 5 1 5


So, our hypothetical student did better than expected, as the answer to 21 or the questions was C. Therefore, the raw score is 21-(59*1/4), which is 6.25 or 25/4. So the winner of the 5/16 FOF Highlander, with a guess of 6, only .25 off, is

Pumpy Tudors!

Congrats!

Just for fun, the raw score our hypothetical student received of 6.25 would get him/her between a 280-320 on this section of the SAT.

[Vince]

Yeah, my quick mental math gave me 16 correct answers and 64 incorrect answers (correct), and that the 64 incorrect answers would result in a penalty of 8 points (incorrect). I thought I'd gamble and go one point higher with a guess of 9. I realized my mistake about 15 seconds after I sent the PM, but figured I'd go with my original guess anyhow.

Good little challenge.

[SackAttack]

Oh, I see. We were guessing the student's raw score, not answering what the raw score should be on average if he dialed down the center.

/duh

[wbatl1]

Oh, I see. We were guessing the student's raw score, not answering what the raw score should be on average if he dialed down the center.

/duh

Well, your guess was right if everything went according to exact probablitites:D

[SackAttack]

Well, your guess was right if everything went according to exact probablitites:D

What do you mean, exact probabilities aren't? RECOUNT! :D

[QuikSand]

with a guess of 6, only .25 off

*sigh*

[wbatl1]

What do you mean, exact probabilities aren't? RECOUNT! :D

I can't tell if your kidding or really upset, but the exact probablities for each question were used, but over 80 questions, 16 didn't come out to each answer because the number generator is random.

[Pumpy Tudors]

Wow, I won something! I'll think up a similar random math puzzle and post it late tonight or early in the morning.

[SackAttack]

I can't tell if your kidding or really upset, but the exact probablities for each question were used, but over 80 questions, 16 didn't come out to each answer because the number generator is random.

upset? that would be this smiley: :mad:

Or something similarly tantrumeriffic. ;)