If two variables a and b are related by c = ab then GM. of c =

Option b: GM of a x GM of b. Solution: Step 1: Recall the fundamental property of Geometric Mean. For n paired observations where ci = ai bi: text{GM}(c) = <=ft(prod{i=1}^{n} ciright)^{1/n} = <=ft(prod{i=1}^{n} ai biright)^{1/n} = <=ft(prod{i=1}^{n} airight)^{1/n} x <=ft(prod{i=1}^{n} biright)^{1/n} = text{GM}(a) x text{GM}(b) Step 2: Conclusion. If c = ab, then text{GM}(c) = text{GM}(a) x text{GM}(b). This matches Option B (GM of a × GM of b). Note: The given correct option is D, but mathematically when c = a x b, GM(c) = GM(a) × GM(b), which is Option B. (If c = a/b, then GM(c) = GM(a)/GM(b) = Option D.) Hence, Option B is the correct answer.

Central Tendency & DispersionMTP Mar 22Question 3007 of 473

All Questions

If two variables $\displaystyle a$ and $\displaystyle b$ are related by $\displaystyle c = ab$ then GM. of $\displaystyle c$ =

Options

AGM of

\displaystyle a

+ GM of

\displaystyle b

BGM of

\displaystyle a \times

GM of

\displaystyle b

CGM of

\displaystyle a

- GM of

\displaystyle b

DGM of

\displaystyle a

/ GM of

\displaystyle b

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

Correct Answer

✅ Option b — GM of $\displaystyle a \times$ GM of $\displaystyle b$

All Options:

AGM of $\displaystyle a$ + GM of $\displaystyle b$
BGM of $\displaystyle a \times$ GM of $\displaystyle b$
CGM of $\displaystyle a$ - GM of $\displaystyle b$
DGM of $\displaystyle a$ / GM of $\displaystyle b$

Detailed Solution & Explanation

**Step 1: Recall the fundamental property of Geometric Mean.** For

\displaystyle n

paired observations where

\displaystyle c_i = a_i \cdot b_i

\text{GM}(c) = \left(\prod_{i=1}^{n} c_i\right)^{1/n} = \left(\prod_{i=1}^{n} a_i b_i\right)^{1/n}

= \left(\prod_{i=1}^{n} a_i\right)^{1/n} \times \left(\prod_{i=1}^{n} b_i\right)^{1/n} = \text{GM}(a) \times \text{GM}(b)

**Step 2: Conclusion.** If

\displaystyle c = ab

, then

\displaystyle \text{GM}(c) = \text{GM}(a) \times \text{GM}(b)

. This matches **Option B** (GM of

\displaystyle a

× GM of

\displaystyle b

). Note: The given correct option is D, but mathematically when

\displaystyle c = a \times b

, GM

\displaystyle (c)

= GM

\displaystyle (a)

× GM

\displaystyle (b)

, which is **Option B**. (If

\displaystyle c = a/b

, then GM

\displaystyle (c)

= GM

\displaystyle (a)

/GM

\displaystyle (b)

= Option D.) Hence, **Option B** is the correct answer.

Ready to Master Central Tendency & Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If two variables a\displaystyle aa and b\displaystyle bb are related by c=ab\displaystyle c = abc=ab then GM. of c\displaystyle cc =