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31 Dec 2023, 09:14
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E
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Difficulty:
85%
(hard)
Question Stats:
48% (02:34) correct
52%
(01:51)
wrong
based on 132
sessions
History
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If a certain tree reached a height of 78 inches by the end of 2023, did it grow by less than 15 inches that year?
(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
31 Dec 2023, 09:14
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Official Solution:
If a certain tree reached a height of 78 inches by the end of 2023, did it grow by less than 15 inches that year?
Assume the height of the tree at the end of 2022 was \(h\) inches. The question then becomes whether \(h + 15 > 78\), or equivalently, whether \(h > 63\).
(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
This implies \(1.3h > 78\), which simplifies to \(h > 60\). This information alone is not sufficient to determine whether \(h > 63\).
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
This implies \(1.2h < 78\), which simplifies to \(h < 65\). This information alone is also not sufficient to determine whether \(h > 63\).
(1)+(2) Combining the statements, we find \(60 < h < 65\). However, this range still does not conclusively answer whether \(h > 63\).
Answer: E
If a certain tree reached a height of 78 inches by the end of 2023, did it grow by less than 15 inches that year?
Assume the height of the tree at the end of 2022 was \(h\) inches. The question then becomes whether \(h + 15 > 78\), or equivalently, whether \(h > 63\).
(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
This implies \(1.3h > 78\), which simplifies to \(h > 60\). This information alone is not sufficient to determine whether \(h > 63\).
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
This implies \(1.2h < 78\), which simplifies to \(h < 65\). This information alone is also not sufficient to determine whether \(h > 63\).
(1)+(2) Combining the statements, we find \(60 < h < 65\). However, this range still does not conclusively answer whether \(h > 63\).
Answer: E
07 Aug 2024, 09:56
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