If x = 2 then f(x) = 8/31 and f(1/x) = -8/31 which is equal to -f(x)
If f(x) = x^3/(x^5 - 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) 
(A)

Answer = C. 110 miles
Relational speed = 120 - 100 = 20 miles per hour
In 4 hours, difference = 20 * 4 = 120 miles
Fast train trailing 10 miles, so effective difference = 120 - 10 = 110 miles
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 120 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 6 o'clock?
Options:
(A) 60 miles
(B) 80 miles
(C) 110 miles
(D) 120 miles
(E) 400 miles
(C)

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

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) 6/19
(B) 6/11
(C) 6/12
(D) 6/10
(E) 6/38
(B)