Every day, Fred takes the train to travel from his work back to Alkmaar, his place of residence. Usually, he arrives at the station of Alkmaar at six o'clock, and exactly at that moment, his wife picks him up by car. Yesterday evening, Fred took an earlier train, without informing his wife, and therefore he already was at the station of Alkmaar at five o'clock. He decided to walk part of the way to meet his wife. When he met the car with his wife, he drove home with her. In this way, they were home ten minutes earlier than normal. Fred's wife always drives the entire way between home and station at the same constant speed.How long did Fred walk yesterday evening?
Options:
(A) 55
(B) 45
(C) 58
(D) 65
(E) 59
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Fred's wife needed to drive ten minutes less than usual, which is five minutes less in the direction of the station and five minutes less back home. Therefore, Fred met his wife at five minutes to six. He had walked already since five o'clock, so he walked 55 minutes in total. So the answer is: (A).
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A pharmaceutical company received $3 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
Options:
(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 56%
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First $20 million: royalties/sales ratio = 3/20 = 36/240
Next $108 million: royalties/sales ratio = 9/108 = 1/12 = 20/240 So the answer is: (C).
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A 2015 model car had an average mileage of 38 miles per gallon, when the car wight was 180 kilograms. An upgraded version of the car in 2016 gave a mileage of 43 miles per gallon and the car weight was reduced to 150 kilograms. By approximately what percent did the mileage of the car to the weight of the car improve?
Options:
(A) 28
(B) 43
(C) 36
(D) 19
(E) 37
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Initial mileage/weight ratio = 38/180 = 190/900
Revised mileage/weight ratio = 43/150 = 258/900 So the answer is: (C).
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