Question

Which of the following statements based on the given table is correct?
$\begin{array}{cccccc}x& 1& 2& 3& 4& 6\\ y& 24& 12& 8& 6& 4\\ \frac{1}{y}& \frac{1}{24}& \frac{1}{12}& \frac{1}{8}& \frac{1}{6}& \frac{1}{4}\end{array}$
I. $x$ and $y$ are directly proportional.
II. $x$ and $y$ are inversely proportional.
III. $x$ and $\frac{1}{y}$ are directly proportional.
IV. All of the above.

• A. Only statement II.
• B. Only statement IV.
• C. Statements I and III.
• D. Statements II and III.

Answer 1

The correct option is D Statements II and III.

$\begin{array}{cccccc}x& 1& 2& 3& 4& 6\\ y& 24& 12& 8& 6& 4\\ \frac{1}{y}& \frac{1}{24}=0.04& \frac{1}{12}=0.08& \frac{1}{8}=0.125& \frac{1}{6}=0.167& \frac{1}{4}=0.25\end{array}$
In the given table, as $x$ increases, $y$ decreases. Hence, $x$ and $y$ are inversely proportional and not directly proportional. Also, as $x$ increases,$\frac{1}{y}$ also increases, which means $x$ and $\frac{1}{y}$ are directly proportional.