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[GMAT math practice question]
(Geometry) In the figure, what is \(BD^2 - CD^2\)?
5.11PS.png [ 5.49 KiB | Viewed 2087 times ]
1) \(AB = 8, AC = 5\)
2) \(AD\) is perpendicular \(BC\)
(Geometry) In the figure, what is \(BD^2 - CD^2\)?
Attachment:
5.11PS.png [ 5.49 KiB | Viewed 2087 times ]
1) \(AB = 8, AC = 5\)
2) \(AD\) is perpendicular \(BC\)
Updated on: 03 Jan 2021, 03:57
Originally posted by MathRevolution on 17 May 2020, 19:49.
Last edited by MathRevolution on 03 Jan 2021, 03:57, edited 1 time in total.
Last edited by MathRevolution on 03 Jan 2021, 03:57, edited 1 time in total.
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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 many variables to determine a function, 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)
\(f(13)=\frac{f(10) - 1}{f(10) + 1}=\frac{11 - 1}{11 + 1}=\frac{5}{6}.\)
\(f(16)=\frac{f(13) - 1}{f(13) + 1}=\frac{5}{6} - 1/\frac{5}{6} + 1=\frac{-1}{11}.\)
\(f(19)=\frac{f(16)-1}{f(16)+1}=\frac{-1}{11}-1/\frac{-1}{11}+1=\frac{-6}{5}\)
\(f(22)=\frac{f(16) - 1}{f(16) + 1}=\frac{-6}{5} - 1/\frac{-6}{5} + 1=11.\)
Since we have \(2008 = 4*5002 + 0\) has a remainder \(0\) when it is divided by \(4\),\( f(2008) = f(16) = \frac{-1}{11}.\)
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.
17 May 2020, 19:53
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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 \(5\) variables (\(AB, BD, CD, CA\), and \(AD\)) and \(0\) equations, 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.
Attachment:
5.11PS(A).png [ 9.14 KiB | Viewed 2034 times ]
Conditions 1) & 2)
Since triangles \(ABD\) and \(ACD\) are right triangles, we have \(AB^2 = BD^2 + AD^2\) and \(AC^2 = CD^2 + AD^2.\) Rearranging the equations gives us \(BD^2 = AB^2 – AD^2\) and \(CD^2 = AC^2 – AD^2. \)
Subtracting the equations gives us \(BD^2 – CD^2 = (AB^2 - AD^2) – (AC^2 – AD^2) = AB^2 - AC^2 = 64 - 25 = 39.\)
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.
