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A certain airline's fleet consisted of 60 type A planes at [#permalink]
09 Jan 2013, 19:42

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00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

65% (02:42) correct
35% (01:45) wrong based on 253 sessions

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

I solved this method using a chart interested in the algebraic approach

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]
09 Jan 2013, 20:46

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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. _________________

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]
09 Jan 2013, 20:48

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fozzzy wrote:

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

I solved this method using a chart interested in the algebraic approach

60 - 3*n = 4*n , n = 60/7 = 8.5

So, in 8.5 years, there would be equal number of planes A & B(which is of course a hypothetical situation).

So, in 9 years the number of B would be more.

Answer is D. _________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]
22 Jan 2015, 08:43

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So, I also created a table, since for me this was faster and safer than venturing an equation. True, in many cases an equation is the only way to reach an answer in good time, but there is no reason to torture yourself with finding one if you have another option and you cannot readily come up with the correct equation! Right??

______A:60 - 3 per year____B: 0 + 4 per year Year1______57_______________4 Year2______54_______________8 Year3______51_______________12 Year4______48_______________16 Year5______45_______________20 Year6______42_______________24 Year7______39_______________28 Year8______36_______________32 Year9______33_______________36

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]
10 Jan 2013, 07:04

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Let x = number of years. Each year we lose 3 Type A planes and gain 4 Type B planes. Since we start off with 60 type A planes and 0 Type B planes, the following equation would determine the point in time where Type A planes = Type B planes (60-3x) = 4x....this comes to 8 4/7 years. Since we are looking for the number of years (rounded to the nearest whole number) where <50% of the planes are of Type A, this must be > 8 years. So 9 years.

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]
09 Jan 2013, 20:55

PraPon wrote:

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, Number Type A with annual rate 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.

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]
09 Jan 2013, 22:29

bhavinshah5685 wrote:

PraPon wrote:

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, Number Type A with annual rate 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.

It should by TYPE B, isnt it?

Thanks. You are right. Its a typo. I have updated the thread. _________________

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]
20 Nov 2013, 06:53

fozzzy wrote:

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

I solved this method using a chart interested in the algebraic approach

Very nice problem fozzy, congrats! Now this is basically an algebraic translation and that's all we need to do so let's go and nail this