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.

Measures of Central Tendency and DispersionMCQMTP 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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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