q: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 36 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) 106.25
(B) 105.5
(C) 105.75
(D) 106
(E) 105.0
a: OK... Rate of flow of water in second hour = 36 gallons per hour
Rate of flow of water in first hour = 36/(3/2) = 24 gallons per hour
Rate of flow of water in third hour = (125/100)* 36 = (5/4) * 36 = 45 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 24+36+45 = 105 gallons
The answer is (E).

q: Fifteen coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^9
(B) 2^14
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
a: OK... Fix the third coin as H. The remaining 14 coins have 2^14 outcomes.
The answer is (B).

q: At the A-Street Fish Market a vendor sells fresh caught fish. His store is filled with 2/7 bass, 1/5 tuna, 1/7 trout, and the rest are catfish. If a customer just bought 1/7 of all the tuna and 1/7 of all the catfish, and a fisherman arrived to restock the bass, doubling the number of bass, what proportion of fish now in the store are trout?
Options:
(A) 30/71
(B) 4/7
(C) 5/43
(D) 1/2
(E) 1/5
a:
OK... Bass = 2/7 = 10/35
Tuna = 1/5 = 7/35
Trout = 1/7 = 5/35
Catfish = 1 - (10/35 +7/35 + 5/35) = 13/35
Purchased: Tuna = 7/35 - (7/35)(1/7) = 6/35, and
Catfish = 13/35 - (13/35)(1/7) = 12/35
Stocked: doubling the number of bass (2)(10/35) = 20/35
Now: 20 + 6 + 5 + 12 = 43
Trout proportion is now 5/43.
The answer is (C).