If Rx and Ry denote ranges of x and y respectively where x and y are related by 4x+5y+12=0, what would be the relation between Rx and Ry?

Option b: 4Rx = 5Ry. Solution: We are given the relationship between x and y: 4x + 5y + 12 = 0 implies 5y = -4x - 12 implies y = -4/5x - 2.4 Since range is independent of change of origin but affected by change of scale, the range of y (Ry) is related to the range of x (Rx) by: Ry = |a| x Rx implies Ry = <=ft|-4/5right| Rx implies Ry = 4/5Rx implies 5Ry = 4Rx This can also be written as 4Rx = 5Ry. Hence, Option B is the correct answer.

If $R_x$ and $R_y$ denote ranges of $x$ and $y$ respectively where $x$ and $y$ are related by $4x+5y+12=0$, what would be the relation between $R_x$ and $R_y$?

The correct answer is Option b: $4R_x = 5R_y$. We are given the relationship between $x$ and $y$: $$4x + 5y + 12 = 0 \implies 5y = -4x - 12 \implies y = -\frac{4}{5}x - 2.4$$ Since range is independent of change of origin but affected by change of scale, the range of $y$ ($R_y$) is related to the range of $x$ ($R_x$) by: $$R_y = |a| \times R_x \implies R_y = \left|-\frac{4}{5}\right| R_x \implies R_y = \frac{4}{5}R_x \implies 5R_y = 4R_x$$ This can also be written as $4R_x = 5R_y$. Hence, **Option B** is the correct answer.

Central Tendency & DispersionMTP Nov 20 Series IIQuestion 3089 of 473

All Questions

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 $\displaystyle 4x+5y+12=0$ , what would be the relation between $\displaystyle R_x$ and $\displaystyle R_y$ ?

Options

\displaystyle R_x = R_y

\displaystyle 4R_x = 5R_y

\displaystyle 5R_x = 4R_y

DNone of these

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Correct Answer

✅ Option b — $\displaystyle 4R_x = 5R_y$

All Options:

A $\displaystyle R_x = R_y$
B $\displaystyle 4R_x = 5R_y$
C $\displaystyle 5R_x = 4R_y$
DNone of these

Detailed Solution & Explanation

We are given the relationship between

\displaystyle x

and

\displaystyle y

4x + 5y + 12 = 0 \implies 5y = -4x - 12 \implies y = -\frac{4}{5}x - 2.4

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

\displaystyle y

(

\displaystyle R_y

) is related to the range of

\displaystyle x

(

\displaystyle R_x

) by:

R_y = |a| \times R_x \implies R_y = \left|-\frac{4}{5}\right| R_x \implies R_y = \frac{4}{5}R_x \implies 5R_y = 4R_x

This can also be written as

\displaystyle 4R_x = 5R_y

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

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