q: In b is a positive integer smaller than 200 and (14b)/60 is an integer, then b has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
a: Stream of consciousness: 7b/30 tells us that b 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: An archer is shooting arrows from various distances. She shoots at a target from 60 yards, 70 yards, and 80 yards. The probability that she hits within the bullseye from 60 yards is 2/3, the probability that she hits within the bullseye from 70 yards is 3/5, and the probability that she hits within the bullseye from 80 yards is 1/2. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
(A) 19/20
(B) 29/30
(C) 49/50
(D) 9/10
(E) 14/15
answer: Stream of consciousness: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 60 yards)*(prob that she misses from 70 yards)*(prob that she misses from 80 yards)
Prob that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5; Prob that she misses from 80 yards = 1 - 1/2 = 1/2
Thus the probability that she misses all shots = (1/3)*(2/5)*(1/2) = 2/30 = 1/15
Thus the probability that she makes at least one shot = 1 - (1/15) = 14/15 The answer is (E).

q: A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work?
Options:
(A) 1
(B) 6
(C) 7
(D) 5
(E) 43
a: Stream of consciousness: A's 1 day work = 1/10; B's 1 day work = 1/15
(A + B)'s 1 day work = (1/10 + 1/15) = 1/6
So, both together will finish the work in 6 days. The answer is (B).

question: 3 friends A, B, C went for week end party to McDonald's restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 140kg then find the average weight of all the 7 rounds?
Options:
(A) 98.5 kgs
(B) 80 kgs
(C) 76.5 kgs
(D) 67.5 kgs
(E) 58.2 kgs
answer: Stream of consciousness: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 140/7 = 80 kgs The answer is (B).

q: How much is 35% of 40 is greater than 4/5 of 25?
Options:
(A) 29
(B) 776
(C) 66
(D) 14
(E) 99
a: Stream of consciousness: (80/100) * 40 (4/5) * 25
35 - 20 = 14 The answer is (D).

q: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is:
Options:
(A) 15
(B) 18
(C) 20
(D) 22
(E) 24
a:
Stream of consciousness: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20 The answer is (C).