The relationship between P-series and Q-series is given by 2P - 3Q - 10 = 0 . If the range of P-series is 18 . What would be the range of Q?

Option d: 12. Solution: Step 1: Express Q in terms of P. From 2P - 3Q - 10 = 0 : Q = 2P - 10/3 = 2/3P - 10/3 Step 2: Apply the range transformation rule. If Q = aP + b , then Range (Q) = |a| × Range (P) . Here a = 2/3 , b = -10/3 . Step 3: Calculate Range of Q. Range(Q) = ≤ft|2/3| × 18 = 2/3 × 18 = 12 Hence, Option D is the correct answer.

The relationship between P-series and Q-series is given by $2P - 3Q - 10 = 0$. If the range of P-series is $18$. What would be the range of Q?

The correct answer is Option d: 12. **Step 1: Express Q in terms of P.** From $2P - 3Q - 10 = 0$: $$Q = \frac{2P - 10}{3} = \frac{2}{3}P - \frac{10}{3}$$ **Step 2: Apply the range transformation rule.** If $Q = aP + b$, then Range$(Q) = |a| \times$ Range$(P)$. Here $a = \frac{2}{3}$, $b = -\frac{10}{3}$. **Step 3: Calculate Range of Q.** $$\text{Range}(Q) = \left|\frac{2}{3}\right| \times 18 = \frac{2}{3} \times 18 = 12$$ Hence, **Option D** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Jan. 21Question 3076 of 473

All Questions

The relationship between P-series and Q-series is given by $\displaystyle 2P - 3Q - 10 = 0$ . If the range of P-series is $\displaystyle 18$ . What would be the range of Q?

Options

A10

B15

D12

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

Correct Answer

✅ Option d — 12

All Options:

Detailed Solution & Explanation

**Step 1: Express Q in terms of P.** From

\displaystyle 2P - 3Q - 10 = 0

Q = \frac{2P - 10}{3} = \frac{2}{3}P - \frac{10}{3}

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

\displaystyle Q = aP + b

, then Range

\displaystyle (Q) = |a| \times

Range

\displaystyle (P)

. Here

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

\displaystyle b = -\frac{10}{3}

. **Step 3: Calculate Range of Q.**

\text{Range}(Q) = \left|\frac{2}{3}\right| \times 18 = \frac{2}{3} \times 18 = 12

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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The relationship between P-series and Q-series is given by 2P−3Q−10=0\displaystyle 2P - 3Q - 10 = 02P−3Q−10=0. If the range of P-series is 18\displaystyle 1818. What would be the range of Q?