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16 Sep 2014, 00:42
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Which of the following points is not on the line \(y = 5x + 3\)?
A. \((\frac{1}{2}, \ \frac{11}{2})\)
B. \((\frac{1}{3}, \ \frac{14}{3})\)
C. \((\sqrt{8}, \ 3 + 10*\sqrt{2})\)
D. \((\sqrt{4}, \ 13)\)
E. \((\sqrt{2}, \ \frac{31}{3})\)
A. \((\frac{1}{2}, \ \frac{11}{2})\)
B. \((\frac{1}{3}, \ \frac{14}{3})\)
C. \((\sqrt{8}, \ 3 + 10*\sqrt{2})\)
D. \((\sqrt{4}, \ 13)\)
E. \((\sqrt{2}, \ \frac{31}{3})\)
16 Sep 2014, 00:42
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Official Solution:
Which of the following points is not on the line \(y = 5x + 3\)?
A. \((\frac{1}{2}, \ \frac{11}{2})\)
B. \((\frac{1}{3}, \ \frac{14}{3})\)
C. \((\sqrt{8}, \ 3 + 10*\sqrt{2})\)
D. \((\sqrt{4}, \ 13)\)
E. \((\sqrt{2}, \ \frac{31}{3})\)
Note that for a point \((x, y)\) to lie on the line \(y = 5x + 3\), the coordinates \(x\) and \(y\) must satisfy the equation \(y = 5x + 3\). It is important to recognize that if \(x\) is an irrational number, then \(5x + 3\) will also be irrational, and as a result, \(y\) must be an irrational number as well. Conversely, if \(x\) is a rational number, then \(y\) must also be a rational number. Among the given options, only option E, \((\sqrt{2}, \ \frac{31}{3})\), violates this rule: \(x\) is irrational while \(y\) is rational. Therefore, for option E \((y = \text{rational}) \neq (5x + 3 = \text{irrational})\), which means that the point \((\sqrt{2}, \ \frac{31}{3})\) does not lie on the line \(y = 5x + 3\).
Note that while Geometry is not tested on GMAT Focus, coordinate geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.
Answer: E
Which of the following points is not on the line \(y = 5x + 3\)?
A. \((\frac{1}{2}, \ \frac{11}{2})\)
B. \((\frac{1}{3}, \ \frac{14}{3})\)
C. \((\sqrt{8}, \ 3 + 10*\sqrt{2})\)
D. \((\sqrt{4}, \ 13)\)
E. \((\sqrt{2}, \ \frac{31}{3})\)
Note that for a point \((x, y)\) to lie on the line \(y = 5x + 3\), the coordinates \(x\) and \(y\) must satisfy the equation \(y = 5x + 3\). It is important to recognize that if \(x\) is an irrational number, then \(5x + 3\) will also be irrational, and as a result, \(y\) must be an irrational number as well. Conversely, if \(x\) is a rational number, then \(y\) must also be a rational number. Among the given options, only option E, \((\sqrt{2}, \ \frac{31}{3})\), violates this rule: \(x\) is irrational while \(y\) is rational. Therefore, for option E \((y = \text{rational}) \neq (5x + 3 = \text{irrational})\), which means that the point \((\sqrt{2}, \ \frac{31}{3})\) does not lie on the line \(y = 5x + 3\).
Note that while Geometry is not tested on GMAT Focus, coordinate geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.
Answer: E
12 Apr 2016, 09:05
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D does not work either
