Airline fleet problem

[abhi.iitb]

Need help in the above question. As per the language of the question(How many years did it take before the number of type A planes left in the Airline's fleet was less than 50% of the fleet) I think answer should be "C". But OA is "D"

[GMATGuruNY]

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.

[GMATGuruNY]

Need help in the above question. As per the language of the question(How many years did it take before the number of type A planes left in the Airline's fleet was less than 50% of the fleet) I think answer should be "C". But OA is "D"

According to the problem, planes are retired and acquired at the END of each year.
As shown in my post above, at the END of the 9th year, there are more Type B planes than Type A planes.
Thus, 9 years must pass BEFORE -- at the END of the 9th year -- there are more Type B planes than Type A planes.

[misterholmes]

I would just observe that each year there is 1 net new plane. So at year 6, there are 66 planes in total, of which 24 are type B. This is, by sight, less than 50%.
Then I would continue in the same fashion, testing the answer choices. For example, for year 8, there are 68 planes, of which 32 are type B. This is still easily seen to be less than half.

Wiki O
For the GMAT Dojo.

[abhi.iitb]

Thanks a lot Mitch for the solution. But, my confusion is in the language of the question stem which says" How many years did it take before the number of type A planes left in the Airline's fleet was less than 50% of the fleet". So, As per my understanding question in other words is asking till how many years Airline fleet has more type A plane than type B plane and answer for that should be 8 not 9. Is in not what the question means here??

Abhishek

Need help in the above question. As per the language of the question(How many years did it take before the number of type A planes left in the Airline's fleet was less than 50% of the fleet) I think answer should be "C". But OA is "D"

According to the problem, planes are retired and acquired at the END of each year.
As shown in my post above, at the END of the 9th year, there are more Type B planes than Type A planes.
Thus, 9 years must pass BEFORE -- at the END of the 9th year -- there are more Type B planes than Type A planes.

[GMATGuruNY]

Thanks a lot Mitch for the solution. But, my confusion is in the language of the question stem which says" How many years did it take before the number of type A planes left in the Airline's fleet was less than 50% of the fleet". So, As per my understanding question in other words is asking till how many years Airline fleet has more type A plane than type B plane and answer for that should be 8 not 9. Is in not what the question means here??

Abhishek

It took x years BEFORE y happened means that y happened AFTER x years had passed.
Here, Type A planes constituted less than half the fleet at the end of the 9th year.
At the end of the 9th year, 9 years had passed.
Thus, it took 9 years before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet.

[[email protected]]

Hi abhi.iitb,

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.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[abhi.iitb]

Thanks a lot Mitch. I understood it now, I was some how confused with the wording of the problem.







It took x years BEFORE y happened means that y happened AFTER x years had passed.
Here, Type A planes constituted less than half the fleet at the end of the 9th year.
At the end of the 9th year, 9 years had passed.
Thus, it took 9 years before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet.

[abhi.iitb]

HI Rich,
Thanks for the solution. I was actually confused with the wording of the question stem.

Hi abhi.iitb,

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.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

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 the number of 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. In other words, we need to determine the number of years it took for the number of type A planes to be less than type B planes. 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 type B planes in the fleet is 4n.

We can create the following equation:

60 - 3n < 4n


60 < 7n

n > 60/7

n > 8 4/7

Since n > 8 4/7, the smallest integer value that n can be is 9.

Answer: D