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: Find 95 97
Options:
(A) 92/198
(B) 92/12
(C) 92/13
(D) 92/10
(E) 92/15
a: Stream of consciousness: Here both numbers are less than 100. So they are deficient of - 5 and - 3 compared with 100. So The answer is (E).

question: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 24 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
Options:
(A) 61.25
(B) 62.5
(C) 63.75
(D) 70.0
(E) 77.5
answer: Stream of consciousness: Rate of flow of water in second hour = 24 gallons per hour
Rate of flow of water in first hour = 24/(3/2) = 16 gallons per hour
Rate of flow of water in third hour = (125/100)* 24 = (5/4) * 24 = 30 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 16+24+30 = 70 gallons The answer is (D).

q: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
(A) 12 days
(B) 15 days
(C) 18 days
(D) 20 days
(E) 22 days
a: Stream of consciousness: A's two day's work = 2/20 = 1/10
(A + B + C)'s one day's work = 1/20 + 1/30 + 1/60 = 6/60 = 1/10
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days
Therefore, Whole work will be done in (3 x 5) = 15 days. The answer is (C).

question: At a meeting of the 3 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 3 Chiefs of Staff be seated around a circular table?
Options:
(A) 120
(B) 480
(C) 960
(D) 2520
(E) 5040
answer: Stream of consciousness: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer C (960), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect? The answer is (C).

question: 10 people meet and shake hands. The maximum number of handshakes possible if there is to be no "cycle" of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, , ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, , {ak-1, ak}, {ak, a1} shake hands).
Options:
(A) 7
(B) 6
(C) 9
(D) 8
(E) 10
answer:
Stream of consciousness: The question is not written in proper manner but we can work in 3 methods
1) If these are random handshakes, then total methods = 10*9/2*1 = 45
2) If these are cyclic handshakes, then total methods = 10
3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9 The answer is (C).