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. text{GM} = (40 x 50 x x)^{1/3} = 10 Step 2: Cube both sides. 40 x 50 x x = 10^3 = 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.

Central Tendency & DispersionMTP 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.

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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