If the AM and HM of two numbers are 6 and 9 respectively, then GM is

Option a: 7.35. Solution: Step 1: Recall the relationship AM × HM = GM². For two numbers, the relationship between AM, GM, and HM is: GM2 = AM × 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 GM = sqrt(54) = 3sqrt(6) ≈ 7.35 Step 3: Match with options. GM ≈ 7.35 = Option A ( 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.

Measures of Central Tendency and DispersionMCQPYQ Nov 20Question 3030 of 473

All Questions

If the AM and HM of two numbers are $\displaystyle 6$ and $\displaystyle 9$ respectively, then GM is

Options

A7.35

B8.5

C6.75

DNone of these

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

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:

\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)

\text{GM}^2 = 6 \times 9 = 54

\text{GM} = \sqrt{54} = 3\sqrt{6} \approx 7.35

**Step 3: Match with options.**

\displaystyle \text{GM} \approx 7.35

= **Option A** (

\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.

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 AM and HM of two numbers are 6\displaystyle 66 and 9\displaystyle 99 respectively, then GM is