If the relationship between x and y is given by 2x + 3y = 10 and the range of y is 10 , then what is the range of x ?

Option d: 15. Solution: Step 1: Express x in terms of y . From 2x + 3y = 10 : x = 10 - 3y/2 = 5 - 3/2y Step 2: Apply the range transformation rule. If x = a + by , then Range (x) = |b| × Range (y) . Here b = -3/2 . Step 3: Calculate Range of x . Range(x) = ≤ft|-3/2| × 10 = 3/2 × 10 = 15 Hence, Option D is the correct answer.

If the relationship between $x$ and $y$ is given by $2x + 3y = 10$ and the range of $y$ is $10$, then what is the range of $x$?

The correct answer is Option d: 15. **Step 1: Express $x$ in terms of $y$.** From $2x + 3y = 10$: $$x = \frac{10 - 3y}{2} = 5 - \frac{3}{2}y$$ **Step 2: Apply the range transformation rule.** If $x = a + by$, then Range$(x) = |b| \times$ Range$(y)$. Here $b = -\frac{3}{2}$. **Step 3: Calculate Range of $x$.** $$\text{Range}(x) = \left|-\frac{3}{2}\right| \times 10 = \frac{3}{2} \times 10 = 15$$ Hence, **Option D** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ July 21Question 3077 of 473

All Questions

If the relationship between $\displaystyle x$ and $\displaystyle y$ is given by $\displaystyle 2x + 3y = 10$ and the range of $\displaystyle y$ is $\displaystyle 10$ , then what is the range of $\displaystyle x$ ?

Options

A10

B18

D15

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 15

All Options:

Detailed Solution & Explanation

**Step 1: Express

\displaystyle x

in terms of

\displaystyle y

.** From

\displaystyle 2x + 3y = 10

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

**Step 2: Apply the range transformation rule.** If

\displaystyle x = a + by

, then Range

\displaystyle (x) = |b| \times

Range

\displaystyle (y)

. Here

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

. **Step 3: Calculate Range of

\displaystyle x

.**

\text{Range}(x) = \left|-\frac{3}{2}\right| \times 10 = \frac{3}{2} \times 10 = 15

Hence, **Option D** 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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If the relationship between x\displaystyle xx and y\displaystyle yy is given by 2x+3y=10\displaystyle 2x + 3y = 102x+3y=10 and the range of y\displaystyle yy is 10\displaystyle 1010, then what is the range of x\displaystyle xx?