question:A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 30 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 7 hours. Harvesting machine K harvested how many acres of wheat per hour?
Options:
(A) 7
(B) 8
(C) 12
(D) 3
(E) 15
answer:(D)
Stream of consciousness:Rate of H = 7 acres/hr
Remaining land to be harvested = 100 - 30 = 70
Rate of H and K = 70/7 = 10 acres/hr
Rate of K = 10 - 7 = 3

question:A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 20
(B) 99
(C) 88
(D) 77
(E) 66
answer:(B)
Stream of consciousness:1: 2/5 = 5: 2
2/7 * 70 = 20

question:If 23m n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
(A) 2m 1
(B) 4m
(C) 6m
(D) m/5
(E) 8m
answer:
(E)
Stream of consciousness:23m - n = p
Add n to both sides:
23m = n + p
Add m to both sides:
24m = n + p + m
Now, divide both sides by 3
8m = (n + p + m)/3 = the average of n, p, and m