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03 Jan 2020, 00:40
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[GMAT math practice question]
(Geometry) The figure shows right triangle \(ABC\) and \(AB = 5, BC = 4\) and \(CA = 3.\) What is the area of triangle \(BDE\)?
1.3ds.png [ 22.3 KiB | Viewed 1509 times ]
1) \(AC = AD\)
2) \(AB\) is perpendicular to \(DE\)
(Geometry) The figure shows right triangle \(ABC\) and \(AB = 5, BC = 4\) and \(CA = 3.\) What is the area of triangle \(BDE\)?
Attachment:
1.3ds.png [ 22.3 KiB | Viewed 1509 times ]
1) \(AC = AD\)
2) \(AB\) is perpendicular to \(DE\)
05 Jan 2020, 00:44
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MathRevolution
=>
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.
Since we have \(9\) variables from \(3\) triangles and \(2\) equations from two right triangles, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2)
Since we have \(AB = AC\) from condition 1) and \(∠DBA = ∠EAC\), the triangles \(ADB\) and \(CEA\) are congruent.
Thus, \(DE = DA + AE = CE + BD = 3 + 4 = 7.\)
Since both conditions together yield a unique solution, they are sufficient.
Therefore, C is the answer.
Answer: C
In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.
05 Jan 2020, 00:47
Kudos
Bookmarks
MathRevolution
=>
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.
Since we have \(2\) variables (\(AD\) and \(EC\)) in the original condition, C is most likely the answer. We can figure out where \(D\) and \(E\) are by \(AD\) and \(EC\). So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2)
Attachment:
ds(a).png [ 15.79 KiB | Viewed 1491 times ]
Since triangles \(AED\) and \(AEC\) are congruent, we have \(DE = CE\) and \(DB = 5 - 3 = 2.\)
The area of triangle \(ABC = (\frac{1}{2})*4*3 = 6\), which is also the sum of the areas of triangle \(ABE\) and triangle \(AEC.\)
Then we have \((\frac{1}{2})*5*DE + (\frac{1}{2})*3*CE = (\frac{5}{2})DE + (\frac{3}{2})DE = (\frac{8}{2})DE = 4DE = 6.\)
Thus, we have \(DE = \frac{6}{4}\), or \(DE = \frac{3}{2}.\)
The area of triangle \(DBE\) is \((\frac{1}{2})*DB*DE = (\frac{1}{2})*2*(\frac{3}{2}) = \frac{3}{2}.\)
Since both conditions together yield a unique solution, they are sufficient.
Therefore, C is the answer.
Answer: C
In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.
