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31 Jan 2016, 07:26
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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:
45%
(medium)
Question Stats:
57% (01:13) correct
43%
(01:16)
wrong
based on 130
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What is the area of the shaded portion of the half-circle?
(1) B is the midpoint of AC.
(2) Angle ABC is a right angle
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31 Jan 2016, 16:35
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What is the area of the shaded portion of the half-circle?
Area= Area of triangle-18pi
(1) B is the midpoint of AC.
We know that 1/2 of the large triangle is a 45-45-90 triangle so we know the side of the 1/2 triangle is 6, 6, 6sqrt(2)
Sufficient
(2) Angle ABC is a right angle
We know that 1/2 of the large triangle is a 45-45-90 triangle so we know the side of the 1/2 triangle is 6, 6, 6sqrt(2)
Sufficient
Answer: D
01 Feb 2016, 05:54
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
What is the area of the shaded portion of the half-circle?
(1) B is the midpoint of AC.
(2) Angle ABC is a right angle
In the original condition, once you know AB, you can figure out the shaded portion(since the angle B=90). So, there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), AB=6√2, which is unique and sufficient.
For 2), you already know that ABC=90, which is not sufficient.
Therefore, the answer is A.
-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
What is the area of the shaded portion of the half-circle?
(1) B is the midpoint of AC.
(2) Angle ABC is a right angle
In the original condition, once you know AB, you can figure out the shaded portion(since the angle B=90). So, there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), AB=6√2, which is unique and sufficient.
For 2), you already know that ABC=90, which is not sufficient.
Therefore, the answer is A.
-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
