q: In e is a positive integer smaller than 200 and (14e)/60 is an integer, then e has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
a: Stream of consciousness: 7e/30 tells us that e 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: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
Options:
(A)  4
(B)  9
(C) 6
(D)  10
(E)  12
answer: Stream of consciousness: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides and added top and bottom, hence 4+2 = 6. The answer is (C).


q: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 400 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
(A) 240
(B) 246
(C) 252
(D) 292
(E) 298
a: Stream of consciousness: Number of newborns that can die in first month = 1/10 * 400 = 40
Survived = 360
Number of newborns that can die in second month = 1/10 * 360 = 36
Survived = 324
Number of newborns that can die in third month = 1/10 * 324 = 32
Survived = 292 The answer is (D).


question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
(A) 7 days
(B) 8 days
(C) 5 days
(D) 4 days
(E) 2 days
answer: Stream of consciousness: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days The answer is (B).


q: Four of the following five are alike in a certain way and so form a group. which one does not belong to that group?
Options:
(A) Tooth
(B) Chin
(C) Nose
(D) Eye
(E) Hand
a: Stream of consciousness: All others have two vowels each The answer is (B).


q: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Options:
(A) 11
(B) 12
(C) 30
(D) 98
(E) 15
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: 20 + 24 + 8 * 2 = 60/2 = 30 The answer is (C).