Q: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 8 businessmen, how many possible team submissions are possible?
Options:
(A) 76
(B) 100
(C) 164
(D) 198
(E) 202
A: OK... Stream of consciousness: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 8C2 = 112
2) 2 tech1 businessman: 4C2 x 8C1 = 48
3) 3 tech0 businessmen: 4C3 = 4
Total: 112+48+4 = 164
The answer is (C).

Q: If x and y are unique prime integers, which of the following must be odd?
Options:
(A) xy^2
(B) 2x+2y
(C) 2x2y
(D) 2x/2y
(E) xy
A: OK... Stream of consciousness: Any number multiplied by 2 has to be an even number henc
The answer is (E).

Q: Guna has 8 flavors of ice cream in him parlor. How many options are there for Thilak to pick a one-flavor, two-flavor, three-flavor, four-flavor, five-flavor, six-flavor,seven-flavor or eight-flavor order?
Options:
(A) 223
(B) 395
(C) 448
(D) 774
(E) 835
A: OK... Stream of consciousness: 8C1 + 8C2+ 8C3+8C4+8C5+8C6+8C7+8C8 = 395.
The answer is (B).

Q: Consider a quarter of a circle of radius 20. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
Options:
(A) 20*(sqr2 -1)
(B) 8*(sqr3 -1)
(C) 4*(sqr7 - 1)
(D) 12* (sqr7 -1)
(E) None of these
A:
OK... Stream of consciousness: I got 20/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
The answer is (A).