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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.
(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.
01 May 2025, 03:25
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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
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09 Jul 2025, 18:25
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Great question. At statement 1 I read "60 times GREATER than". That led me to miss but I think it was a good question though. Tks
