question: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 30, and 40 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
Options:
(A)  4/11
(B)  1/2
(C)  15/22
(D)  120/7
(E)  11/4
answer: Stream of consciousness: P1 takes 12 hrs
Rate for P2P3 together = 1/30 + 1/40 = 7/120
Therefore they take 120/7
Ratio = 120/7 = The answer is (D).


q: Divide Rs.32000 in the ratio 3:7?
Options:
(A) 12000, 20000
(B) 9600, 22400
(C) 12000, 20007
(D) 12000, 20006
(E) 12000, 20001
a: Stream of consciousness: 3/10 * 32000 = 9600
7/8 * 32000 = 22400 The answer is (B).


question: George's car calls for 8 ounces of oil for each cylinder used. His car's engine has 6 cylinders. If 16 ounces of oil has already been put into the engine used, then how many additional ounces of oil are needed?
Options:
(A) 16
(B) 48
(C) 64
(D) 32
(E) 8
answer: Stream of consciousness: Number of ounces per cylinder 8
Number of cylinders 6
Ounces needed 48
Ounces used 16 The answer is (D).


q: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
(A) 17 1/7
(B) 17 1/5
(C) 17 1/8
(D) 17 1/1
(E) 17 1/2
a: Stream of consciousness: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days The answer is (A).


question: A train does a journey without stoppage in 8 hours, if it had travelled 5 km/h faster, it would have done the journey in 6 hours 40 minutes. Find its original speed.
Options:
(A) 25 km/h
(B) 40 km/h
(C) 45 km/h
(D) 36.5 km/h
(E) None of these
answer: Stream of consciousness: Let original speed = S km/h
Here, distance to be covered is constant
∴ S × 8 = (S + 5)(20⁄3)
⇒ 8S - 20⁄3S = 100⁄3 ⇒ S = 100⁄4 = 25 km/h The answer is (A).


question: If f(x) = x^4/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) f(x) 
(B) 1/-f(x) 
(C) -2/-f(x) 
(D) -3/-f(x) 
(E) -f(x) 
answer:

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: If x = 2 then f(x) = 16/15 and f(1/x) = -16/15 which is equal to -f(x) The answer is (E).