question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 4 hours. Harvesting machine K harvested how many acres of wheat per hour?
Options:
(A) 7
(B) 8
(C) 11
(D) 13
(E) 15
answer: Stream of consciousness: Rate of H = 4 acres/hr
Remaining land to be harvested = 100 - 40 = 60
Rate of H and K = 60/4 = 15 acres/hr
Rate of K = 15- 4 = 11 The answer is (C).

q: Grace has 17 jellybeans in her pocket. She has 9 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) 14
(E) 16
a: Stream of consciousness: The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. The answer is (D).

question: 9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?
Options:
(A) 23
(B) 30
(C) 42
(D) 60
(E) 126
answer: Stream of consciousness: Out of 6 gaurds we have to select 3 -> selection means we use C -> so 6C3
Out of 3 forwards we have to select 2 -> selection means we use C -> so 3C2
Total ways = 6C3 x 3C2 = 60 The answer is (D).

q: The average of seven results is 156 and that of the first six is 169. The fifth result is?
Options:
(A) 120
(B) 160
(C) 89
(D) 78
(E) 148
a: Stream of consciousness: 7 * 156 6 * 169 = 78 The answer is (D).

question: In g is a positive integer smaller than 200 and (14g)/60 is an integer, then g has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
answer: Stream of consciousness: 7g/30 tells us that g is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3. The answer is (B).

question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?
Options:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
answer:
Stream of consciousness: Mother has a fixed place and father, so there are 2! ways to arrange the children, hence The answer is (A).