The geometric mean of the numbers 40, 50 , and x is 10 , and the value of x is

Option d: 1/2. Solution: Step 1: Set up the equation. GM = (40 × 50 × x)1/3 = 10 Step 2: Cube both sides. 40 × 50 × x = 103 = 1000 2000x = 1000 x = 1000/2000 = 1/2 = 0.5 Step 3: Identify the answer. x = 1/2 , which corresponds to Option D ( 1/2 ). Note: The given correct option is C ( 2 ), but mathematically x = 1/2 = Option D. Hence, Option D is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 22 - Series IQuestion 3009 of 473

All Questions

The geometric mean of the numbers $\displaystyle 40, 50$ , and $\displaystyle x$ is $\displaystyle 10$ , and the value of $\displaystyle x$ is

Options

\displaystyle 1/2

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Correct Answer

✅ Option d — $\displaystyle 1/2$

All Options:

A5
B4
C2
D $\displaystyle 1/2$

Detailed Solution & Explanation

**Step 1: Set up the equation.**

\text{GM} = (40 \times 50 \times x)^{1/3} = 10

**Step 2: Cube both sides.**

40 \times 50 \times x = 10^3 = 1000

2000x = 1000

x = \frac{1000}{2000} = \frac{1}{2} = 0.5

**Step 3: Identify the answer.**

\displaystyle x = \frac{1}{2}

, which corresponds to **Option D** (

\displaystyle 1/2

). Note: The given correct option is C (

\displaystyle 2

), but mathematically

\displaystyle x = 1/2

= **Option D**. 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 geometric mean of the numbers 40,50\displaystyle 40, 5040,50, and x\displaystyle xx is 10\displaystyle 1010, and the value of x\displaystyle xx is