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A certain airline's fleet consisted of 60 type A planes at

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

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New post 13 Sep 2018, 23:12
Hi,

While the tabular and algebraic approach are discussed, we can look at this question in another way.

So when ever 3 Type A are removed they are replaced with 4 of type B. So every year there will be 1 more aircraft in the fleet than previous year.

And for 60 planes to go to 50 % of its value which is 30 , it would take 10 years. But in 10 years the fleet size would be 60 +1* 10= 70 .
So definitely 30 is way less than 50% of the fleet

In 8 years Type A would be 24 less than today which is = 36 and Total fleet size would be 60+8= 68. But 50% of 68 is 34 but type a is more than 50 %

So in 9 Years it would have reduced by 27 which is 33, and fleet size would be 60+9= 69. 50%* 69= 34.5 So type A less than 50 %

hence D

Or You could set up an equation like this

No of planes in given year n = 60-3n+4n

Essentially We can say no of planes 1 year i.e 1980 = 61 and number of Type A = 60-3n =57 when n =1

So in 6,7,8,9,10 years it will be 66,67,68,69 70 receptively and number of type A aircraft would be 42,39,36,33,30 respectively.

So We see that by year 9 Type A aircraft are less than 50 % of total number of aircraft

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

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New post 25 Mar 2019, 05:03
From the question, we understand that the increase in the fleet is directly related to the number of years.
For example: End of 1979 Fleet: 60, End of 1980 Fleet : 61 {60 + ( - 3typeA + 4typeB ) } i.e 60 + 1 with 4 type B.
We need to find the year at which the number of Type A planes is lesser than 50 % of the fleet.
To find: No. of Type A planes < .5(60+No of years)

Through the options,
After 8 years : Fleet - 60 + 8 {Type B = (8 * 4) =32 , remaining are the type A planes i.e. 36 planes} 36> .5(68)
After 9 years : Fleet - 60 +9 { Type B = (9*4)= 36 , remaining are the type B planes i.e. 33 planes } Suffiicient, since 33 < .5(69)
Ans : D : 9 Years
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Re: A certain airline's fleet consisted of 60 type A planes at  [#permalink]

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New post 26 Mar 2019, 22:30
x < 50% (x+y) ----> x< y

n = no of years

60 - 3n < 4n
60 < 7n

n >= 9
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A certain airline's fleet consisted of 60 type A planes at  [#permalink]

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New post 28 Apr 2019, 10:46
With the explanations, I have see many different equalities used. I understand that there is (almost) always more than 1 way to solve a GMAT problem.

But is there an expert who can provide some light into the situation?

I used the inequality as noted above, but I see many explanations which all seem to give the same answer


\(60-3t < 4t\)
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Re: A certain airline's fleet consisted of 60 type A planes at  [#permalink]

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New post 27 Jun 2019, 17:31
Type A remaining / Type A remaining + Type B acquired
Type A remaining = 60-3y (y=years)
Type B acquired = 4y

60-3y / 60-3y + 4y < 1/2
60-3y / 60+y < 1/2
120-6y < 60+y
60 < 7y
60/7 < y
8 4/7 < y
We round up to 9 because we need more than 8 years to get rid of 4/7 more A planes, thus D.
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A certain airline's fleet consisted of 60 type A planes at  [#permalink]

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New post 13 Aug 2019, 18:02
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



We know that the original # of planes is 60, we lose 3 Type A planes per year, and gain 4 Type B plans. We want to find when the RATIO of \(\frac{# of Type A Planes}{Total Number of Planes}\) when it's less than \(\frac{1}{2}\)

To translate that into words:

\(\frac{60 - 3x}{60-3x+4x}\) < \(\frac{1}{2}\)

\(120-6x\) < \(60+x\)

\(60\) < \(7x\)

\(X > 60/7\)

Closest Multiple of 7 that's greater than 60 is 63, so 63/7 = 9 years

Answer is D
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A certain airline's fleet consisted of 60 type A planes at   [#permalink] 13 Aug 2019, 18:02

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