Central Tendency & DispersionMTP May 20Question 3085 of 473

If $\displaystyle R_x$ and $\displaystyle R_y$ denote ranges of $\displaystyle x$ and $\displaystyle y$ respectively where $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 3x+2y+10=0$ , what would be the relation between $\displaystyle x$ and $\displaystyle y$ ?

\displaystyle R_x = R_y

\displaystyle 2R_x = 3R_y

\displaystyle 3R_x = 2R_y

\displaystyle R_x = 2R_y

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Correct Answer

✅ Option c — $\displaystyle 3R_x = 2R_y$

We are given the linear relationship between variables

\displaystyle x

and

\displaystyle y

3x + 2y + 10 = 0 \implies 2y = -3x - 10 \implies y = -\frac{3}{2}x - 5

Since range is independent of change of origin but affected by change of scale, for

\displaystyle y = ax + b

, the range is related by:

R_y = |a| \times R_x

Substitute

\displaystyle a = -\frac{3}{2}

R_y = \left|-\frac{3}{2}\right| \times R_x \implies R_y = \frac{3}{2}R_x \implies 2R_y = 3R_x

Hence, **Option C** is the correct answer.

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