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 5y = -4x - 12 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| × Rx Ry = ≤ft|-4/5| Rx Ry = 4/5Rx 5Ry = 4Rx This can also be written as $4Rx = 5Ry$. Hence, Option B is the correct answer.

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

The correct answer is Option b: $4Rx = 5Ry$. We are given the relationship between x and y : 4x + 5y + 12 = 0 5y = -4x - 12 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| × Rx Ry = ≤ft|-4/5| Rx Ry = 4/5Rx 5Ry = 4Rx This can also be written as $4Rx = 5Ry$. 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 $4x+5y+12=0$, what would be the relation between $R_x $\displaystyle and$ R_y$?

Select Your Answer (Keyboard: A, B, C, D)

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Correct Answer

✅ Option b — $4R_x = 5R_y$

All Options:

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

Detailed Solution & Explanation

\displaystyle x

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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If Rx\displaystyle R_xRx​ and Ry\displaystyle R_yRy​ denote ranges of x\displaystyle xx and y\displaystyle yy respectively where x\displaystyle xx and y\displaystyle yy are related by $4x+5y+12=0$, what would be the relation between $R_xand\displaystyle andandR_y$?