2003 CEMC Pascal Problems/Problem 6

Problem

Which of the following is not equal to $\frac{18}{5}$ ?

$\text{ (A) }\ \frac{6^2}{10} \qquad\text{ (B) }\ \frac{1}{5}[6(3)]) \qquad\text{ (C) }\ \frac{18 + 1}{15 + 1} \qquad\text{ (D) }\ 3.6 \qquad\text{ (E) }\ \sqrt{\frac{324}{5}}$

Solution

We can simply try answer choices until we get one that isn't equal to $\frac{18}{5}$ :

$\frac{6^2}{10} = \frac{36}{10} = \frac{36 \div 2}{10 \div 2} = \frac{18}{5}$

$\frac{1}{5}[6(3)]) = \frac{1}{5} \times 18 = \frac{18}{5}$

$\frac{18 + 1}{15 + 1} = \frac{19}{16} \neq \frac{18}{5}$

This shows us that the answer is $\boxed {\textbf {(C) } \frac{18 + 1}{15 + 1}}$ .

We can also verify that the others are equal to $\frac{18}{5}$ :

$3.6 = \frac{36}{10} = \frac{18}{5}$

From $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ , we have:

$\sqrt{\frac{324}{25}} = \frac{\sqrt{324}}{\sqrt{25}} = \frac{18}{5}$

~anabel.disher

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2003 CEMC Pascal Problems/Problem 6

Problem

Solution