AMS 303 SECOND TEST REVIEW Solutions to Past Tests


Spring 2016 AMS 303 Second Test
1.(4 pts) TeS A: (x sub 3)^2; Test B: (x sub3)^2.
2. 2. Test A (12 pts) a (-,oo), b(h-,1), c(g-,1), d(i-,1), e(i-,1), f(a+,1), g(b+,1) h(f+,1), i(f+,1), j(c+ or e+,1), k(d+,1), z(g+,1). One new solution using c-j is b-g, c-j, d-i, e-k, f-h; other is b-h, c-g, d-k, e-j, f-i.
Test B (15 pts) a) initial digital sum is 011 = 3; b) remove 3 from pile 2 or remove 1 from pile 3 or 4; c) remove 2 from pile 2 or 3 or 4; d) g(0)=0, g(1)=1, g(2)=0, g(3)=1, g(4)=0, g(5)=1, g(6)=2, sum is 11, remove 5 from pile 4.
Test A (15 pts) a) initial digital sum is 011 = 3; b) remove 3 from pile 2 or remove 1 from pile 3 or 4; c) remove 2 from pile 1 or 3 or 4; d) g(0)=0, g(1)=1, g(2)=0, g(3)=1, g(4)=2, g(5)=3, g(6)=2, sum is 1, remove 1 from pile 4 or remove 5 from pile 4.
Test B (12 pts) a (-,oo), b(h-,1), c(i-,1), d(j-,1), e(k-,1), f(a+,1), g(b+ or d+,1) h(c+,1), i(f+,1), j(e+,1), k(f+,1), z(g+,1). One new solution using b-g is b-g, c-h, d-j, e-k, f-i, other is b-h, c-i, d-g, e-j, f-k.
4. Test A (12 pts) (1/4)[(b+w)^5 +3(b+w)(b^2 + w^2)^2].
Test B (10 pts) Initial solution: x11=20, x12=10, x22=10, x23=20, x33=20. Prices u1=$10, u2=$11, u3=$13, v1=$14, v2=$17, v3=$18. Select x13. Increase x13 and x22 by 10, reduce x12 and x23 by 10.
5. Test A ( 8 pts) Possible. Number of available wins (L 2, T 2, V 3) equals number of games to be played. Many possible solutions.
Test B (8 pts) Not possible, L and V play 4 games but have only 3 available wins (L 2, V 1).
6. Test A (10 pts) Initial solution: x11=20, x12=10, x22=20, x23=20, x33=20. Prices u1=$10, u2=$8, u3=$10, v1=$15, v2=v3=$14. Select either x13 or x31. For x13, increase x13 and x22 by 10, reduce x12 and x23 by 10. For x31, increase x31, x12, x23 by 20, reduce x11, x22, x22 by 20.
Test B (12 pts) (1/4)[(b+w)^5 + 3(b+w)(b^2 + w^2)^2].


Spring 2015 AMS 303 Second Test
1. x sub 10
2. a) digital sum of piles is 011=3, b) remove 3 from pile 3, c) take 1 from pile 3, d) g(0)=0, g(1)=1, g(2)=0, g(3)=1, g(4)=2, g(5)=3, g(6)=2, g(7)=0, sum is 10, remove 4 from pile 1.
3. a (-,oo), b(g-,1), c(h-,1), d(i-,1), e(j-,1), f(a+,1), g(c+) h(f+,1), i(f+,1), j(d+,1), k(b+ or e+,1), z(k+,1). One new solution b-k, c-g, d-i, e-j, f-h)
4.(1/8)[(b+w)^12 + 2(b^4+w^4)^3 + 3(b^2+w^2)^6 + 2(b+w)^2(b^2+w^2)^5].
5. Not possible,L & T play 4 games but they can collectively only win 3 games.
6. Initial solution: x11=30, x21=30, x22=20, x23=10, x33=20. Prices u1=$10, u2=$9, u3=$12, v1=$15, v2=14, v3=16. Select x13. Increase x13 and x21 by 10, reduce x11 and x23 by 10.

Spring 2013 AMS 303 Second Test
1. x sub 9.
2. a (-,oo), b(a+,1), c(j-,1), d(h-,1), e(i-,1), f(k-,1), g(e+ or f+,1) h(b+,1), i(c+,1), j(b+,1), k(d+,1), z(g+,1). One new solution b-j, c-i, d-h, e-g, f-k.
3. a) digital sum of piles is 011=3, b) remove 3 from pile 2 or 3, b) take 1 from pile 2, c) g(0)=0, g(1)=1, g(2)=2, g(3)=0, g(4)=1, g(5)=2, g(6)=0, g(7)=1, sum is 01, remove 1 from pile 3.
4.(1/4)[(b+w)^9 +(b+w)(b^2 + w^2)^4 +2(b+w)^3(b^2 + w^2)^3].
5. Not possible,L & T play 3 games but each can win only 1 game.
6. Initial solution: x11=40, x12=30, x22=10, x32=20, x33=40. Prices u1=$10, u2=$9, u3=$11, v1=v3=$15, v2=14. Select x13. Increase x13 and x32 by 30, reduce x12 and x33 by 30.