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24 Dec 2019, 09:04
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
61% (00:50) correct
39%
(01:00)
wrong
based on 49
sessions
History
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What is the area of a regular hexagon?
(1) The length of the boundary line of the hexagon is 36 cm.
(2) The area of the hexagon is 6 times the area of an equilateral triangle formed on one of the sides.
(1) The length of the boundary line of the hexagon is 36 cm.
(2) The area of the hexagon is 6 times the area of an equilateral triangle formed on one of the sides.
24 Dec 2019, 16:35
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
Since a regular polygon has 1 variable, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Since the perimeter of the hexagon is \(36\), the length of one side is \(6\).
The regular hexagon consists of three equilateral triangles with side \(6\).
The area of the equilateral triangle is 9√3 and the area of the hexagon is \(6 \cdot 9√3 = 54√3\).
Since condition 1) yields a unique solution, it is sufficient
Condition 2)
Condition 2) is the natural property of a regular hexagon. It doesn't tell anything about the regular hexagon in this problem.
Then we don't know the length of the regular hexagon and condition 2) is not sufficient.
Therefore, A is the answer.
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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14 Aug 2023, 01:12
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