A certain airline's fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
A. 6
B. 7
C. 8
D. 9
E. 10
We can PLUG IN THE ANSWERS, which represent the number of years required for there to be more Type B planes that Type A planes.
Each year 3 Type A planes are retired, while 4 Type B planes are acquired, for a net GAIN of one plane per year.
Since the fleet is INCREASING to a number GREATER THAN 60 -- and Type B planes must constitute more than half the resulting fleet -- there must be at least 30 Type B planes after the correct number of years.
The answer choices imply that the following numbers of Type B planes are acquired:
A: (6 years)(4 planes per year) = 24.
B: (7 years)(4 planes per year) = 28.
C: (8 years)(4 planes per year) = 32.
The least viable option is C.
Eliminate A and B.
Answer choice C: 8 years
Since 4 Type B planes are acquired each year, the total number of Type B planes after 8 years = 8*4 = 32.
Since 3 of the 60 Type A planes are retired each year, the total number of Type A planes after 8 years = 60 - (8*3) = 36.
Here, there are fewer Type B planes than Type A planes.
Eliminate C.
Answer choice D: 9 years
Since there are 32 Type B planes after 8 years, and 4 more Type B planes are acquired in the 9th year, the total number of Type B planes after 9 years = 32+4 = 36.
Since there are 36 Type A planes after 8 years, and 3 more Type A planes are retired in the 9th year, the total number of Type A planes after 9 years = 36-3 = 33.
Success!
Here, there are more Type B planes than Type A planes.
The correct answer is
D.
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