q: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
(A) 6/15
(B) 6/11
(C) 6/14
(D) 6/12
(E) 6/13
a: OK... Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
The answer is (B).

q: Two persons A and B can complete a piece of work in 15 days and 30 days respectively. If they work together, what part of the work will be completed in 5 days?
Options:
(A) 1/8
(B) 1/3
(C) 1/6
(D) 1/2
(E) 5/3
a: OK... A's one day's work = 1/15
B's one day's work = 1/30
(A + B)'s one day's work = 1/15 + 1/30 = 1/10
The part of the work completed in 5 days = 5 (1/10) = 1/2.
The answer is (D).

q: 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
a:
OK... 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).