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A certain airline's fleet consisted of 60 type A planes at [#permalink]

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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 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]

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09 Jan 2013, 21:46

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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.
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Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]

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09 Jan 2013, 21:48

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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.
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Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]

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09 Jan 2013, 21:55

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]

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09 Jan 2013, 23:29

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.
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Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]

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10 Jan 2013, 08:04

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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]

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20 Nov 2013, 07:53

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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

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

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]

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22 Jan 2015, 09:43

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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

When dealing with questions that can be solved with simple arithmetic and a bit or brute force, it's often best/fastest to just put pen-to-pad and 'map out' the solution. The prompt mentions that planes retired and acquired at the END of each year. You can create a quick table to track what you're looking for:

Start: 60 A and 0 B Yr 1: 57 A and 4 B Yr 2: 54 A and 8 B Yr 3: 51 A and 12 B Yr 4: 48 A and 16 B Yr 5: 45 A and 20 B Yr 6: 42 A and 24 B Yr 7: 39 A and 28 B Yr 8: 36 A and 32 B Yr 9: 33 A and 36 B

After 9 years, the type A planes were less than 50% of the total.

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]

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25 Nov 2015, 17:41

pacifist85 and Rich demonstrate the utility (and power) of simply creating a table of values. For more on using tables to solve quantitative questions, watch the following free video - http://www.gmatprepnow.com/module/gmat- ... /video/929

Re: A certain airline's fleet consisted of 60 type A planes at [#permalink]

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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 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 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
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