Central Tendency & DispersionPYQ Nov 20Question 3030 of 473
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If the AM and HM of two numbers are 6\displaystyle 6 and 9\displaystyle 9 respectively, then GM is

Options

A7.35
B8.5
C6.75
DNone of these
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Correct Answer

✅ Option a — 7.35

All Options:

  • A7.35
  • B8.5
  • C6.75
  • DNone of these

Detailed Solution & Explanation

**Step 1: Recall the relationship AM × HM = GM².** For two numbers, the relationship between AM, GM, and HM is: GM2=AM×HM\text{GM}^2 = \text{AM} \times \text{HM} **Step 2: Substitute values.** - AM = 6, HM = 9 (Note: for two numbers, AM ≥ GM ≥ HM always; here HM > AM which is unusual) GM2=6×9=54\text{GM}^2 = 6 \times 9 = 54 GM=54=36≈7.35\text{GM} = \sqrt{54} = 3\sqrt{6} \approx 7.35 **Step 3: Match with options.** GM≈7.35\displaystyle \text{GM} \approx 7.35 = **Option A** (7.35\displaystyle 7.35). Note: For real positive numbers, AM ≥ GM ≥ HM always. Here HM = 9 > AM = 6, which is not possible for real positive numbers. However, applying the formula mechanically: GM = √(6×9) = √54 ≈ 7.35. Hence, **Option A** is the correct answer.

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