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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
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A certain airline’s fleet consisted of 60 type A planes at the b...
This problem is extremely easy to solve if you leverage the answers by backsolving, but it can be confusing and time-consuming if you try to create an equation or inequality. Since it will be clear on this question if you need a smaller or larger number after your first try at backsolving, start in the middle with (C). In 8 years, there will be 60-8(3) or 36 type A planes and (8)(4) or 32 type B planes. No: B is not greater than A, so you need a larger number. In 9 years, there will be 60 – (9)(3) or 33 type A planes and (9)(4) or 36 type B planes. Jackpot: 9 is the first answer that makes B > A so (D) is correct. You can literally sit back in your chair and do this with very little mental effort in under one minute with backsolving. If you solved this problem in any other way, you simply did not choose the best approach (and there is a good chance you got it wrong or spent 3+ minutes). In other algebraic interpretation questions, it might be better to use algebra—backsolving will be either impractical or impossible—but not so on this question!
In working with students, I use this question to see if they are truly leveraging the full toolbox to solve GMAT quant questions. If you don’t see the easy backsolving approach here, it means you are not looking for it. There are numerous ways to solve GMAT problem solving questions: you can use algebra or other “traditional” math approaches; you can pick numbers to remove abstraction in percent or variable word problems; you can use conceptual thinking or logic; you can actively leverage the answer choices (backsolving).
When GMAT math questions are created, they are designed to punish people who always approach questions the same way. A typical 700+ level question on the exam will make you use fairly hard algebra to go most of the way to the answer, but then the only way to get it correct at the end is to leverage the answers. The problem can’t be solved without answer choices to leverage, yet the “algebra machine” student will knock his or her head against the computer trying to solve the problem in a vacuum without actively using the answers. More commonly, questions are created in which one approach is extremely difficult or time consuming, while another approach is quite simple (as in this question).
In working with students, I use this question to see if they are truly leveraging the full toolbox to solve GMAT quant questions. If you don’t see the easy backsolving approach here, it means you are not looking for it. There are numerous ways to solve GMAT problem solving questions: you can use algebra or other “traditional” math approaches; you can pick numbers to remove abstraction in percent or variable word problems; you can use conceptual thinking or logic; you can actively leverage the answer choices (backsolving).
When GMAT math questions are created, they are designed to punish people who always approach questions the same way. A typical 700+ level question on the exam will make you use fairly hard algebra to go most of the way to the answer, but then the only way to get it correct at the end is to leverage the answers. The problem can’t be solved without answer choices to leverage, yet the “algebra machine” student will knock his or her head against the computer trying to solve the problem in a vacuum without actively using the answers. More commonly, questions are created in which one approach is extremely difficult or time consuming, while another approach is quite simple (as in this question).
Most Upvoted Answer
A certain airline’s fleet consisted of 60 type A planes at the b...
Understanding the problem:
The airline starts with 60 type A planes and at the end of each year, it retires 3 type A planes and acquires 4 new type B planes.
Calculating the number of type A planes over the years:
- Year 1980: 60 type A planes
- Year 1981: 60 - 3 = 57 type A planes
- Year 1982: 57 - 3 = 54 type A planes
- Year 1983: 54 - 3 = 51 type A planes
- Year 1984: 51 - 3 = 48 type A planes
Finding the answer:
After 5 years (by the end of 1984), the number of type A planes is 48, which is less than 50% of the fleet (60/2 = 30). Therefore, it took 5 years for the number of type A planes left in the airline's fleet to be less than 50%.
Conclusion:
The correct answer is option D - 9 years.
The airline starts with 60 type A planes and at the end of each year, it retires 3 type A planes and acquires 4 new type B planes.
Calculating the number of type A planes over the years:
- Year 1980: 60 type A planes
- Year 1981: 60 - 3 = 57 type A planes
- Year 1982: 57 - 3 = 54 type A planes
- Year 1983: 54 - 3 = 51 type A planes
- Year 1984: 51 - 3 = 48 type A planes
Finding the answer:
After 5 years (by the end of 1984), the number of type A planes is 48, which is less than 50% of the fleet (60/2 = 30). Therefore, it took 5 years for the number of type A planes left in the airline's fleet to be less than 50%.
Conclusion:
The correct answer is option D - 9 years.
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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)6b)7c)8d)9e)10Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)6b)7c)8d)9e)10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)6b)7c)8d)9e)10Correct answer is option 'D'. Can you explain this answer?.
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)6b)7c)8d)9e)10Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)6b)7c)8d)9e)10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)6b)7c)8d)9e)10Correct answer is option 'D'. Can you explain this answer?.
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