If \(x\) and \(y\) are directly proportional and when \(x=13\), \(y=39\) , which of the following is not a possible pair of corresponding values of \(x\) and \(y\)?（ ）

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If \(x\) and \(y\) are directly proportional and when \(x=13\), \(y=39\) , which of the following is not a possible pair of corresponding values of \(x\) and \(y\)?（ ）

C

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Given, \(x\) and \(y\) are directly proportional

i.e. \(x\propto y\)

\(\Rightarrow\) \(x=ky\) where \(k\) is constant.

With \(x=13\) and \(y=39\), we have

\(13=39k\)

\(\Rightarrow\) \(k=\frac{13}{39}\)\(\Rightarrow\) \(k=\frac{1}{3}\).

So, \(\frac{x}{y}=\frac{1}{3}\).

Checking all the options as:

a.) \(x=1\) and \(y=3\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 3=1\).

b.) \(x=17\) and \(y=51\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 51=17\)

c.) \(x=30\) and \(y=10\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 10\neq 30\)

d.) \(x=6\) and \(y=18\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 18=6\).

Since option \((C)\) only does not follow the proportionality.

Hence, \((C)\) is the correct option.

i.e. \(x\propto y\)

\(\Rightarrow\) \(x=ky\) where \(k\) is constant.

With \(x=13\) and \(y=39\), we have

\(13=39k\)

\(\Rightarrow\) \(k=\frac{13}{39}\)\(\Rightarrow\) \(k=\frac{1}{3}\).

So, \(\frac{x}{y}=\frac{1}{3}\).

Checking all the options as:

a.) \(x=1\) and \(y=3\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 3=1\).

b.) \(x=17\) and \(y=51\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 51=17\)

c.) \(x=30\) and \(y=10\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 10\neq 30\)

d.) \(x=6\) and \(y=18\), checking with \(k=\frac{1}{3}\)

i.e. \(x=\frac{1}{3}\times 18=6\).

Since option \((C)\) only does not follow the proportionality.

Hence, \((C)\) is the correct option.

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