Central Tendency & DispersionPYQ Jan. 21Question 3076 of 473
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The relationship between P-series and Q-series is given by 2P−3Q−10=0\displaystyle 2P - 3Q - 10 = 0. If the range of P-series is 18\displaystyle 18. What would be the range of Q?

Options

A10
B15
C9
D12
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Correct Answer

✅ Option d — 12

All Options:

  • A10
  • B15
  • C9
  • D12

Detailed Solution & Explanation

**Step 1: Express Q in terms of P.** From 2P−3Q−10=0\displaystyle 2P - 3Q - 10 = 0: Q=2P−103=23P−103Q = \frac{2P - 10}{3} = \frac{2}{3}P - \frac{10}{3} **Step 2: Apply the range transformation rule.** If Q=aP+b\displaystyle Q = aP + b, then Range(Q)=∣a∣×\displaystyle (Q) = |a| \times Range(P)\displaystyle (P). Here a=23\displaystyle a = \frac{2}{3}, b=−103\displaystyle b = -\frac{10}{3}. **Step 3: Calculate Range of Q.** Range(Q)=∣23∣×18=23×18=12\text{Range}(Q) = \left|\frac{2}{3}\right| \times 18 = \frac{2}{3} \times 18 = 12 Hence, **Option D** is the correct answer.

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