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09 Jan 2013, 20:42
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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 planes. 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
PS07066
A. 6
B. 7
C. 8
D. 9
E. 10
PS07066
PrashantPonde
Joined: 27 Jun 2012
Last visit: 29 Jan 2025
Posts: 322
Given Kudos: 185
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Updated on: 09 Jan 2013, 23:51
Originally posted by PrashantPonde on 09 Jan 2013, 21:46.
Last edited by PrashantPonde on 09 Jan 2013, 23:51, edited 3 times in total.
Last edited by PrashantPonde on 09 Jan 2013, 23:51, edited 3 times in total.
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Algebraic approach:
Consider x as number of years when both planes A & B will reach towards their break-even and then type B just exceeds type A planes.
i.e. in x years, The number of Type B planes with annual rate of 4 will be just greater than (existing inventory of 60 planes minus Type A inventory reduced at annual rate 3 in x years)
i.e. \(4x\geq{60 - 3x}\)
i.e. \(7x\geq{60}\)
i.e. \(x\geq{8.57}\)
Round to next integer \(x = 9 years\)
Hence choice(D) is the correct answer.
PS: This problem is similar to water tank problem - one pipe is filling the tank and another one draining at different rate.
Consider x as number of years when both planes A & B will reach towards their break-even and then type B just exceeds type A planes.
i.e. in x years, The number of Type B planes with annual rate of 4 will be just greater than (existing inventory of 60 planes minus Type A inventory reduced at annual rate 3 in x years)
i.e. \(4x\geq{60 - 3x}\)
i.e. \(7x\geq{60}\)
i.e. \(x\geq{8.57}\)
Round to next integer \(x = 9 years\)
Hence choice(D) is the correct answer.
PS: This problem is similar to water tank problem - one pipe is filling the tank and another one draining at different rate.
27 Feb 2017, 11:58
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fozzzy
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
A. 6
B. 7
C. 8
D. 9
E. 10
We are given that the fleet started with 60 type A planes. We are also given that the airline retired 3 of the type A planes and acquired 4 new type B planes each year. We need to determine how many years it took for the number of type A planes left in the airline's fleet to be less than 50 percent of the fleet. We can let n = the number of years it will take for this to occur.
The number of type A planes in the fleet can be expressed as 60 - 3n (because the fleet loses 3 type A planes each year). The total number of planes in the fleet is 60 - 3n + 4n, which takes into account the loss of 3 type A planes and addition of 4 type B planes each year.
We are interested in the number of years it will take until the number of type A planes is less than ½ the total planes in the fleet, as illustrated in the following equation:
60 - 3n < (60 - 3n + 4n) x ½
Multiplying the entire equation by 2, we have:
120 - 6n < 60 + n
-7n < -60
n > -60/-7
n > 8 4/7
Since n > 8 4/7, the smallest integer value n can be is 9.
Answer: D
