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GMAT TIGER

agree with E for the reason given above.

\(\sqrt{2}\) is an irrational number i.e a non-terminating value.

Ah, there's a difference between 'irrational' and 'non-terminating'. 1/3 = 0.33333.... is 'non-terminating', but it is also certainly a rational number. Rational numbers are those that can be written as fractions using only integers. As decimals, rational numbers can be terminating or non-terminating, but when rational numbers produce non-terminating decimals, they *always* produce repeating (sometimes called recurring) decimals; a certain pattern of digits repeats forever. Irrational numbers are those numbers like \(\Pi\) and \(\sqrt{2}\) which cannot be written as fractions involving integers. As decimals, irrational numbers have no pattern of digits that repeats forever.
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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. \((\sqrt{2}, \ \frac{31}{3})\)


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 \(y = 5x + 3\).


Answer: E
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