q: Calculate the circumference of a circular field whose radius is 10 centimeters.
Options:
(A) 20 cm
(B) 19 cm
(C) 28 cm
(D) 25 cm
(E) 30 cm
a: Stream of consciousness: Circumference C is given by
C = 2r = 2*10 = 20 cm The answer is (A).

question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
(A) 63
(B) 25
(C) 40
(D) 65
(E) 98
answer: Stream of consciousness: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63. The answer is (A).

q: A, B and C can do a work in 8 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
Options:
(A) 3
(B) 2 2/8
(C) 2 2/0
(D) 2 2/2
(E) 2 2/1
a: Stream of consciousness: Work done by all three of them in one day = 1/8 + 1/8 + 1/12 = 1/3
The number of days required = 3 days. The answer is (A).

question: In a race with 30 runners where 8 trophies will be given to the top 8 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 8^8 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
answer: Stream of consciousness: 8 people can be prized with 8 distinct prizes in 8^8 ways The answer is (A).

q: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 2354
(B) 2644
(C) 2645
(D) 4577
(E) 5184
a: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).

q: Grace has 20 jellybeans in her pocket. She has 12 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Options:
(A) 4
(B) 8
(C) 12
(D) 13
(E) 17
a:
Stream of consciousness: The worst scenario is when she takes 12 red and 4 green, total of 16 jellybeans, and still doesn't have 3 distinct colors. But the next draw (17th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. The answer is (E).