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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
60% (02:19) correct
40%
(02:27)
wrong
based on 195
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
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.
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.
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22 Dec 2023, 06:25
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GMAT Club Official Explanation:
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.
General Discussion
21 Dec 2023, 08:03
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Asked: 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.
Let the tree reached a height of x inches by the end of 2022.
1.3x > 78
x > 78/1.3 = 60; x > 60 inches
The tree grew that year = 78-x < 78-60 = 18 inches
If x = 61; The tree grew that year = 78-x = 78-61 = 17 inches > 15 inches
If x = 65; The tree grew that year = 78-x = 78-65 = 13 inches < 15 inches
NOT SUFFICIENT
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
Let the tree reached a height of x inches by the end of 2022.
1.2x < 78
x < 78/1.2 = 65 inches
The tree grew that year = 78-x > 78-65 = 13 inches
If x = 64; The tree grew that year = 78-x = 78-64 = 14 inches < 15 inches
If x = 61; The tree grew that year = 78-x = 78-61 = 17 inches > 15 inches
NOT SUFFICIENT
(1) + (2)
(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
Let the tree reached a height of x inches by the end of 2022.
1.3x > 78
x > 78/1.3 = 60; x > 60 inches
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
1.2x < 78
x < 78/1.2 = 65 inches
60<x<65;
If x = 64; The tree grew that year = 78-x = 78-64 = 14 inches < 15 inches
If x = 61; The tree grew that year = 78-x = 78-61 = 17 inches > 15 inches
NOT SUFFICIENT
IMO E
(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
Let the tree reached a height of x inches by the end of 2022.
1.3x > 78
x > 78/1.3 = 60; x > 60 inches
The tree grew that year = 78-x < 78-60 = 18 inches
If x = 61; The tree grew that year = 78-x = 78-61 = 17 inches > 15 inches
If x = 65; The tree grew that year = 78-x = 78-65 = 13 inches < 15 inches
NOT SUFFICIENT
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
Let the tree reached a height of x inches by the end of 2022.
1.2x < 78
x < 78/1.2 = 65 inches
The tree grew that year = 78-x > 78-65 = 13 inches
If x = 64; The tree grew that year = 78-x = 78-64 = 14 inches < 15 inches
If x = 61; The tree grew that year = 78-x = 78-61 = 17 inches > 15 inches
NOT SUFFICIENT
(1) + (2)
(1) By the end of 2023, the tree was less than 30 percent higher than by the end of 2022.
Let the tree reached a height of x inches by the end of 2022.
1.3x > 78
x > 78/1.3 = 60; x > 60 inches
(2) In 2023, the tree grew by more than 20 percent of its height by the end of 2022.
1.2x < 78
x < 78/1.2 = 65 inches
60<x<65;
If x = 64; The tree grew that year = 78-x = 78-64 = 14 inches < 15 inches
If x = 61; The tree grew that year = 78-x = 78-61 = 17 inches > 15 inches
NOT SUFFICIENT
IMO E
