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01 May 2025, 03:28
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
45% (02:45) correct
55%
(02:18)
wrong
based on 93
sessions
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During a wildlife monitoring study, the population of red-tailed hawks in a region decreased by 20%, while the population of gray foxes increased by 20% over the same period. At the end of the study, was the population of gray foxes greater than the population of red-tailed hawks?
(1) At the start of the study, the red-tailed hawk population was 60 greater than the gray fox population.
(2) The gray fox population increased by a number equal to 25 percent of the number by which the red-tailed hawk population decreased.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
(1) At the start of the study, the red-tailed hawk population was 60 greater than the gray fox population.
(2) The gray fox population increased by a number equal to 25 percent of the number by which the red-tailed hawk population decreased.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
10 May 2025, 20:30
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Official Solution:
During a wildlife monitoring study, the population of red-tailed hawks in a region decreased by 20%, while the population of gray foxes increased by 20% over the same period. At the end of the study, was the population of gray foxes greater than the population of red-tailed hawks?
Let the red-tailed hawk population at the start be H, and the gray fox population at the start be F. The question asks: Is 1.2 * F > 0.8 * H? This simplifies to: Is 3F > 2H?
(1) At the start of the study, the red-tailed hawk population was 60 greater than the gray fox population.
Just knowing the initial difference is not enough to answer the question. For example, if H = 100 and F = 40, the answer is No. But if H = 1000 and F = 940, the answer is Yes. Not sufficient.
(2) The gray fox population increased by a number equal to 25 percent of the number by which the red-tailed hawk population decreased.
This means that 0.2 * F = 0.25 * (0.2 * H), which simplifies to H = 4F. Substituting into the question: Is 3F > 2H? becomes: Is 3F > 8F. This is never true, so the answer is always No. (Or even without that: if the hawk population was four times the fox population, then even after decreasing by 20% and the fox population increasing by 20%, hawks would still be more.) Sufficient.
Answer: B
During a wildlife monitoring study, the population of red-tailed hawks in a region decreased by 20%, while the population of gray foxes increased by 20% over the same period. At the end of the study, was the population of gray foxes greater than the population of red-tailed hawks?
Let the red-tailed hawk population at the start be H, and the gray fox population at the start be F. The question asks: Is 1.2 * F > 0.8 * H? This simplifies to: Is 3F > 2H?
(1) At the start of the study, the red-tailed hawk population was 60 greater than the gray fox population.
Just knowing the initial difference is not enough to answer the question. For example, if H = 100 and F = 40, the answer is No. But if H = 1000 and F = 940, the answer is Yes. Not sufficient.
(2) The gray fox population increased by a number equal to 25 percent of the number by which the red-tailed hawk population decreased.
This means that 0.2 * F = 0.25 * (0.2 * H), which simplifies to H = 4F. Substituting into the question: Is 3F > 2H? becomes: Is 3F > 8F. This is never true, so the answer is always No. (Or even without that: if the hawk population was four times the fox population, then even after decreasing by 20% and the fox population increasing by 20%, hawks would still be more.) Sufficient.
Answer: B
General Discussion
05 May 2025, 23:06
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Bunuel
Before study
Population of red-tailed hawks = h
Population of gray foxes = f
After study
Population of red-tailed hawks = 0.8h
Population of gray foxes = 1.2f
Question
\(1.2f > 0.8h\)
\(\frac{f}{h} > \frac{0.8}{1.2}\)
\(\frac{f}{h} > \frac{2}{3}\)
Statement 1
(1) At the start of the study, the red-tailed hawk population was 60 greater than the gray fox population.
h = f + 60
From this information we cannot find a multiplicative relationship between 'h' and 'f'.
Hence, the statement alone is not sufficient to answer the question asked.
Eliminate A, and D.
Statement 2
(2) The gray fox population increased by a number equal to 25 percent of the number by which the red-tailed hawk population decreased.
Increase in gray fox population = 0.2f
Decrease in red-tailed hawk population = 0.2h
\(0.2f = 0.25 * 0.2h\)
\(\frac{f}{h} = 0.25\)
The statement alone is sufficient to answer whether \(\frac{f}{h} > \frac{2}{3}\)
Option B
