Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.
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Question: Problem: a bottle contains a certain solution. in the bottled solution, the ratio of water to soap is 3: 4, and the ratio of soap to salt is five times this ratio. the solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. at that time, what is the ratio of water to salt in the solution ?
Options: a. 9: 32, b. 9: 30, c. 32: 9, d. 19: 32, e. 18: 30

Answer: a


Question: Problem: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 24 kilometers per hour. the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up ?
Options: a. 10, b. 15, c. 20, d. 25, e. 30

Answer: d


Question: Problem: a solid yellow stripe is to be painted in the middle of a certain highway. if 1 gallon of paint covers an area of w square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long ? ( 1 mile = 5,280 feet and 1 foot = 12 inches )
Options: ['a. ( 5,280 mt ) / 12 w', 'b. ( 5,280 pt ) / 12 m', 'c. ( 5,280 pmt ) / 12', 'd. ( 5,280 ) ( 12 m ) / pt', 'e. ( 5,280 ) ( 12 p ) / mt']

Answer:
a