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A group of entomologists estimates that the population of Insect Species X is decreasing at a constant rate of 10% per year, while the population of Insect Species Y is decreasing at a constant rate of 15% per year. Based on these estimates, in four years, the two species will have equal populations, rounded to the nearest million. In the table below, identify a number for the current population of Insect Species X, in millions, and a number for the current population of Insect Species Y, in millions, that could be consistent with the entomologists’ estimates.
  • a)
    450
  • b)
    525
  • c)
    565
  • d)
    600
  • e)
    625
Correct answer is option 'A,C'. Can you explain this answer?
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Verified Answer
A group of entomologists estimates that the population of Insect Speci...
Insect Species X: Choice A, 450
Insect Species Y: Choice C, 565
First, note that, if the populations are to become equal in four years, at a 10% and a 15% rate of decrease, respectively, then the two populations are not currently equal. Additionally, the current population of Insect Species Y must be more than the current population of Insect Species X, in order for their totals to converge, at these independent rates of decrease, in four years. Therefore, the current population of Insect Species X cannot be 625, and the current population of Insect Species Y cannot be 450.
The problem requires working with two unknowns: the current population of Insect Species X and the current population of Insect Species Y. Therefore, Plug In The Answers to determine which will satisfy the conditions of the question. To approach the problem most efficiently, recognize that a 10% decrease is the same as taking 90% of the original number. Suppose that the current population of Insect Species X is 500. A 10% decrease from 450 is equivalent to 90% of 500, or (.9)(450), which is 405. That would be the decrease for one year. To find the decrease for the next year, you would need to begin with the adjusted population and decrease from there: a 10% decrease from 405 is equivalent to (.9)(405), which is 364.5. So, finding the decrease for two subsequent years from a current population of 450 is equivalent to calculating (.9)(.9)(450) = 364.5. Similarly, finding the decrease for four subsequent years at a 10% rate from a current population of 450 is equivalent to calculating (.9)(.9)(.9)(.9)(450) = (.6561)(450) = 295.245. So, to find the decreased population of Insect Species X for four years at a 10% rate, you would calculate (.6561)(current population X).
A 15% decrease is the same as taking 85% of the original number, so to find the decreased population of Insect Species Y for four years at a 15% rate, you would calculate (.85)(.85)(.85)(.85)(current population Y), or approximately (.522)(current population Y).
To determine what two current populations will be equal (rounded to the nearest million) in four years, you are looking for values that satisfy the equation (0.6561)(current population X) = (0.522)(current population Y). Now you can simply calculate with each value provided to see what the future populations would be:
Rounded to the nearest million, the values that satisfy the equation (0.6561) (current population X) = (0.522)(current population Y) are 450 for the current population of Insect Species X and 565 for the current population of Insect Species Y, which would both decrease to approximately 295 million, at their independent rates of decrease, in four years.
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Most Upvoted Answer
A group of entomologists estimates that the population of Insect Speci...
To solve this problem, let's assume the current population of Insect Species X is 100 million.

After four years, the population of Insect Species X will decrease by 10% each year for four years. This can be calculated as follows:
100 million * (1 - 0.10)^4 = 66.96 million (rounded to the nearest million)

Now, let's assume the current population of Insect Species Y is 200 million.

After four years, the population of Insect Species Y will decrease by 15% each year for four years. This can be calculated as follows:
200 million * (1 - 0.15)^4 = 108.96 million (rounded to the nearest million)

Therefore, a possible consistent scenario could be that the current population of Insect Species X is 67 million (rounded to the nearest million) and the current population of Insect Species Y is 109 million (rounded to the nearest million).
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A group of entomologists estimates that the population of Insect Speci...
Insect Species X: Choice A, 450
Insect Species Y: Choice C, 565
First, note that, if the populations are to become equal in four years, at a 10% and a 15% rate of decrease, respectively, then the two populations are not currently equal. Additionally, the current population of Insect Species Y must be more than the current population of Insect Species X, in order for their totals to converge, at these independent rates of decrease, in four years. Therefore, the current population of Insect Species X cannot be 625, and the current population of Insect Species Y cannot be 450.
The problem requires working with two unknowns: the current population of Insect Species X and the current population of Insect Species Y. Therefore, Plug In The Answers to determine which will satisfy the conditions of the question. To approach the problem most efficiently, recognize that a 10% decrease is the same as taking 90% of the original number. Suppose that the current population of Insect Species X is 500. A 10% decrease from 450 is equivalent to 90% of 500, or (.9)(450), which is 405. That would be the decrease for one year. To find the decrease for the next year, you would need to begin with the adjusted population and decrease from there: a 10% decrease from 405 is equivalent to (.9)(405), which is 364.5. So, finding the decrease for two subsequent years from a current population of 450 is equivalent to calculating (.9)(.9)(450) = 364.5. Similarly, finding the decrease for four subsequent years at a 10% rate from a current population of 450 is equivalent to calculating (.9)(.9)(.9)(.9)(450) = (.6561)(450) = 295.245. So, to find the decreased population of Insect Species X for four years at a 10% rate, you would calculate (.6561)(current population X).
A 15% decrease is the same as taking 85% of the original number, so to find the decreased population of Insect Species Y for four years at a 15% rate, you would calculate (.85)(.85)(.85)(.85)(current population Y), or approximately (.522)(current population Y).
To determine what two current populations will be equal (rounded to the nearest million) in four years, you are looking for values that satisfy the equation (0.6561)(current population X) = (0.522)(current population Y). Now you can simply calculate with each value provided to see what the future populations would be:
Rounded to the nearest million, the values that satisfy the equation (0.6561) (current population X) = (0.522)(current population Y) are 450 for the current population of Insect Species X and 565 for the current population of Insect Species Y, which would both decrease to approximately 295 million, at their independent rates of decrease, in four years.
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A group of entomologists estimates that the population of Insect Species X is decreasing at a constant rate of 10% per year, while the population of Insect Species Y is decreasing at a constant rate of 15% per year. Based on these estimates, in four years, the two species will have equal populations, rounded to the nearest million. In the table below, identify a number for the current population of Insect Species X, in millions, and a number for the current population of Insect Species Y, in millions, that could be consistent with the entomologists’ estimates.a)450b)525c)565d)600e)625Correct answer is option 'A,C'. Can you explain this answer?
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A group of entomologists estimates that the population of Insect Species X is decreasing at a constant rate of 10% per year, while the population of Insect Species Y is decreasing at a constant rate of 15% per year. Based on these estimates, in four years, the two species will have equal populations, rounded to the nearest million. In the table below, identify a number for the current population of Insect Species X, in millions, and a number for the current population of Insect Species Y, in millions, that could be consistent with the entomologists’ estimates.a)450b)525c)565d)600e)625Correct answer is option 'A,C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A group of entomologists estimates that the population of Insect Species X is decreasing at a constant rate of 10% per year, while the population of Insect Species Y is decreasing at a constant rate of 15% per year. Based on these estimates, in four years, the two species will have equal populations, rounded to the nearest million. In the table below, identify a number for the current population of Insect Species X, in millions, and a number for the current population of Insect Species Y, in millions, that could be consistent with the entomologists’ estimates.a)450b)525c)565d)600e)625Correct answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A group of entomologists estimates that the population of Insect Species X is decreasing at a constant rate of 10% per year, while the population of Insect Species Y is decreasing at a constant rate of 15% per year. Based on these estimates, in four years, the two species will have equal populations, rounded to the nearest million. In the table below, identify a number for the current population of Insect Species X, in millions, and a number for the current population of Insect Species Y, in millions, that could be consistent with the entomologists’ estimates.a)450b)525c)565d)600e)625Correct answer is option 'A,C'. Can you explain this answer?.
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