MOEMS Marathon

Thunder365

Solution: $x+y+z=9$ , which has 11C2=55 solutions over 6^3=216 ways. 55/216?

NP:Points A and B lie on a circle of radius 2 and center at O and the measure of angle AOB is 90 degrees. What is the area of the smaller region bounded by the circle and the chord joining A to B?

**Posted:** Tue Oct 13, 2009 3:19 pm

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goldenboy1.618

Solution

NP

**Posted:** Wed Oct 14, 2009 4:44 am

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AwesomeToad

The expected value for who?

**Posted:** Wed Oct 14, 2009 8:14 am

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$LaTeX$

Solution

New Problem

**Posted:** Wed Oct 14, 2009 4:24 pm

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Wallbash Red

DOPE!!! I FAIL AT EVERYTHING!!!
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FlyAgaric

solution (maybe?)

NP: One quiz is worth half of a test. Susan took two quizzes and scored 76 and 82. Then she took a test and scored 79. She has another test coming in a week and wants to raise her average to at least 82. What is the lowest score she could get on the next test?

**Posted:** Tue Oct 20, 2009 1:15 pm

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Fly Agaric (fli-a-ger-ik) n. 1. type of mushroom which is bright red with small white dots; consumption may lead to death or extreme, short-term growth 2. n. a genius

Maybach

Solution
NP

**Posted:** Tue Oct 20, 2009 1:58 pm

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Math Champion

Solution

NP

**Posted:** Tue Oct 20, 2009 2:30 pm

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FlyAgaric

Solution

NP

**Posted:** Tue Oct 20, 2009 2:44 pm

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Fly Agaric (fli-a-ger-ik) n. 1. type of mushroom which is bright red with small white dots; consumption may lead to death or extreme, short-term growth 2. n. a genius

Maybach

Solution
NP

**Posted:** Wed Oct 21, 2009 4:14 pm

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jin thynj · Poincare Conjecture Offline Joined: 04 Apr 2008 Posts: 141

**Posted:** Thu Oct 22, 2009 6:24 pm

jin thynj · Poincare Conjecture Offline Joined: 04 Apr 2008 Posts: 141

NP: I have some red sweets, and you have some blue sweets. Find max{|S|} if S is the set of all possible couples (red sweet, blue sweet) Rolling Eyes

**Posted:** Thu Oct 22, 2009 6:35 pm

cgyao15

hmm... how many sweetw do i have and how many does u have?

**Posted:** Fri Oct 23, 2009 2:29 pm

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Thunder365

Okay, NP:

Find the number of solutions to the equation $2a + 5b = 2009$ for which both $a$ and $b$ are positive integers.

**Posted:** Fri Oct 30, 2009 10:56 am

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MoTheMan · Poincare Conjecture Offline Joined: 03 Oct 2007 Posts: 131

We count 2s:
2 2s and 401 5s
7 2s and 399 5s
..
1002 2s and 1 5
That is 201 solutions.

NP:
Abe and Bob win a Banana Creme-Chocolate Mousse pie worth 18 dollars at the fair. Half of the pie is one flavor and the other half is the other flavor. Abe likes Banana 5 times as much as chocolate and Bob likes Chocolate twice as much as Banana. If Abe cuts it so that he likes each piece the same amount, and one piece is all Banana, and Bob picks the piece that is worth most to him, what value does Bob put on his piece?

**Posted:** Thu Nov 05, 2009 5:30 pm

FlyAgaric

My interpretation:

It is cut into thirds (one banana, one chocolate, one both). Bob picks chocolate because that is his favorite. Since he has 1/3 of the pie, it is worth 6 dollars. However the problem was not very clear.

If Bob thinks chocolate is twice as valuable as banana then he thinks that the chocolate half is worth 12 dollars to him (?) so his slice would be worth 8 dollars to him (it is 2/3 of the chocolate half). I'm not sure though. Huh?

**Posted:** Fri Nov 06, 2009 4:26 pm

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Fly Agaric (fli-a-ger-ik) n. 1. type of mushroom which is bright red with small white dots; consumption may lead to death or extreme, short-term growth 2. n. a genius

MoTheMan · Poincare Conjecture Offline Joined: 03 Oct 2007 Posts: 131

I am sorry. Let me make the problem more clear.
Abe cuts in into two pieces. One piece is a certain amount of banana and no chocolate. The other is all the chocolate and the other bit of banana.
Abe thinks the banana half is 15 dollars and the chocolate half is 3.
Bob thinks the banana half is 6 dollars and the chocolate half is 12.

**Posted:** Sat Nov 07, 2009 5:48 am

FlyAgaric

Ok then

Abe wants both slices to be worth 9 dollars. The all-banana slice is 3/5 of the banana half or 3/10 of the pie. Bob takes the half that is 7/10 of the pie which is worth to him 18-3.60=14.40 dollars.

**Posted:** Sat Nov 07, 2009 7:17 am

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Fly Agaric (fli-a-ger-ik) n. 1. type of mushroom which is bright red with small white dots; consumption may lead to death or extreme, short-term growth 2. n. a genius

steve123456

Post a new NP after you solved one. I'll post this new problem.

NP: Max is on his triangular lawn in his backyard. He labels the vertices of the triangle A , B , and C, with AB=10, BC=15, and AC= 13. Then he draws the angle bisector of A until it intersects with BC at point X. What is the length of AX?

**Posted:** Sat Nov 07, 2009 10:34 am