1) 100 hunters catch 400 mice in 80 hours
How long does it take for 500 hunters to catch 250 mice?
2) Super brie market on discussion board
demand function is Q = 1000 / P + 200
supply function is Q = 2*P - 500
where Q = hourly quantity of super brie and P = price per piece of super brie
What is the super brie price at market equilibrium?
Please round off your answer to four decimal places.
3) Without mousehunters, mouse population doubles every 5 days. Without assassins, mousehunter population doubles every 100 days. State a possible hunting condition that sufficiently makes the mouse population ramain constant.
4) Speaking of our super brie donators, Jadey is taller than Barry but shorter than Emma. Gro's height is exactly the average of Emma's and Laura's. Jadey's height is closest to Gro's, but Laura's height is not closet to Gro's. Laura is not the shortest.
Please rank them in a descending order according to height.
5) How much does a donator, in average, donated to mousehunt math quizzes? (Super brie valued at 400 gold per piece)
Hint: visit the group's page for stats.
6) There are 7 white mice, 9 grey mice, 11 mutated white mice, 13 mutated grey mice.
How many arms, how many ears and how many colors are there in total?
Each mouse has two legs. Please don't be confused with arms.
7) This is from an investigation of Colleen - F.B.I.
A trusted trader always tell the truth.
A scammer always tell the lies.
Matt: I am a scammer OR Mickey is a scammer.
Michael: I am a scammer AND Michelle is a scammer.
Mickey: More than half of us are trusted traders.
Mark: Michelle is a trusted trader.
Mario: Muhammad is a trusted trader.
Muhammad: I am a trusted trader.
Michelle: I love martini, bon bon and M & M. **winks**
Please name all scammers.
8) Once upon a time, there were many bugs in Mousehunt application. Coding devs played bughunt. Dave was using pesticide, Giorgio - a pingpong racket, and Joel - a gun. Joel spotted a bug on Dave's forehead at the same moment that Dave spotted a bug on Giorgio's mustache and that Giorgio spotted a bug between Joel's thighs.
What is the 'aftermath' in your imagination?
9) Please help Townsend decipher King's reward code.
34429 = DIGBY
787372743 = ?
10) At a super brie reverse auction (minimum decrement = 5 gold apiece):
1st bid = x+20 apiece
2nd bid = y-30 apiece
3rd bid = x+y-50 apiece
...
7th bid = 0 apiece (wins)
Plot all possible x's and y's in a graph and calculate the area of the feasible region.
* SOLUTION
*****1)
1 hunter catch 400 mice in 80*100 = 8000 hours
1 hunter catch 1 mouse in 8000/400 = 20 hours
1 hunter catch 250 mice in 20*250 = 5000 hours
500 hunters catch 250 mice in 5000/500 = 10 hours
*****2)
At market equilibrium, quantity demanded = quantity supplied
1000/P + 200 = 2*P - 500
1000 + 200*P = 2*P*P - 500*P
500 + 100*P = P*P - 250*P
P*P - 350*P - 500 = 0
(P + 1.4228) (P - 351.4228) = 0
P + 1.4228 = 0 OR P - 351.4228 = 0
P = -1.4228 OR P = 351.4228
Since a price cannot be negative, P = 351.4228
*****3)
Population growth problem.
Your answer should implicitly or explicitly address that:
(1) Mousehunters can interfere mouse population growth.
(2) Mousehunters do something to mouse population so that net difference between births, deaths and migration is zero.
(3) If there are mousehunters, mouse population increases by its own.
Statement (3) is given, so it should not be contradicted by your answer. The statement also implies that only mousehunters could 'possibly' interfere mouse population growth. Thus, statement (1) should follow.
There are many possibilities to answer this question.
Here is a very simple yet smart answer.
- Immigration of mice is not possible due to powerful military force. Mousehunters capture all the mice and imprison them separately in a controlled environment. Dead mice are immediately replaced by their clones.
Here is a simple answer.
- Immigration is prohibited, all mice are immortal, and mousehunters deport all new-born mice to somewhere outside the "universe" (area of study).
Here is a more complicated answer.
- Migration is prohibited, and 14.8698% of mice are killed by mousehunters every day.
You can calculate daily net growth rate for mouse population.
(1+g)^5 = 2
1+g = 1.148698
g = 14.8698%
We can say that without mousehunters, every day there are roughly 15% more mice.
An even more complicated answer might go through control of population structures in terms of gender and age (mice and mousehunters alike), assumptions of minimum reproduction age, fertility rate and even mouse-catch-per-day-per-hunter rate.
However, no one has gone that far.. lol
*****4)
Emma > Jadey > Barry.
Jadey's height is closest to Gro's. Therefore, Emma > Gro.
Gro's height is exactly the average of Emma's and Laura's. Therefore, Emma > Gro > Laura.
Laura is not the shortest. Therefore, Laura > Barry.
Emma > Jadey > Laura > Barry
Laura's height is not closest to Gro's. As Chew Zi-Yen pointed out, this might not be clear. I tried to mean 'closest' as "adjacent in order"
Answer: Emma > Gro > Jadey > Laura > Barry
*****5)
Last entry is...
SB balance: 255
Gold balance: 230 000
Add up all spendings:
SB balance: 255
Gold balance: 230 000 + 35 287 = 265 287
Total value = 255*400 + 265 287 = 367 287
Average = 367287/7 donators = 52469.5714 pieces of gold per donator
*****6)
White mouse: 2 arms, 2 ears
Grey mouse: 2 arms, 2 ears
Mutated white mouse: 2 arms, 3 ears (one extra ear)
Mutated grey mouse: 5 arms, 2 ears (three extra arms)
7+9+11+13=40 mice have 80 arms and 80 ears...plus 11 extra ears for mutated white mice and 3*13=39 extra arms for mutated grey mice.
Answer: 119 arms, 91 ears and two colors.
*****7)
Logic question. You should know about logical operators. Please search for a wikipedia article "Truth table" for reference.
- Matt cannot be a scammer. If Matt is a scammmer, what he says must be false. That is, he is not a scammer and Mickey is not a scammer. Then this contradicts with our assumption that Matt is a scammer. Thus, Matt is a trusted trader, and Mickey must be a scammer.
- Michael cannot be a trusted trader. If he is a trusted trader, what he says must be true. That is, he is a scammer and Michelle is a scammer. Then this contradicts with our assumption that Matt is a scammer. Thus, Michael is a scammer, and Michelle is a trusted trader.
- Mickey is a scammer. So, we know that from what he says, at least 4 of them are scammers.
- Mark's words confirm that he is a trusted trader.
- Mario's words imply that for Mario and Muhammad, both are trusted trader, or neither are trusted trader.
- So far, we know that Matt, Michelle and Marks are trusted trader while Mickey and Michael are scammers. Because at least 4 of them are scammers, both Mario and Muhammad must be scammers.
Answer: Michael, Mickey, Mario, Muhammad
*****8)
Some of you complained about this question. Have you watched Jurassic Park? A mathematician had predicted that the park would collapse, using "Chaos theory".
But no, we don't go that far. We seem to have a event chain of "circular reference". Joel -> Dave -> Giorgio -> Joel. I expect that you have a mathematical sense of "dynamical systems". In other words, a point's position in its ambiant space depends on time.
For example:
Pesticide has a "butterfly effect" yet accuracy depends greatly on distance.
A gunshot, if Joel decided to shoot, should have happened first if distance between the three was more than a few steps.
Well, to make it easy, I will give some SB to everyone who sent an answer to this question.
*****9)
SUPERBRIE
It's a cellphone dial code. Very easy. I know.
*****10)
We know that first bid must be greater than or equal to 30. Also, first bid must be at least 5 gold apiece more than second bid.
x + 20 >= y - 30 + 5 >= 30
Similarly,
y - 30 >= x + y - 50 + 5 >= 25
x + y - 50 >= 20
After simiplification,
y <= x + 45
15 >= x >= 10
y >= 55
y >= 70 - x
The feasible region is a triangle { (15, 55), (15, 60), (12.5, 57.5) }
Area = 1/2 * base * height = 1/2 * 5 * 2.5 = 6.25 square unit.
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