The harmonic mean A and B is 1/3 and harmonic mean of C and D is 1/5. The harmonic mean of ABCD is

Option b: 1/4. Solution: Step 1: Recall the formula for Harmonic Mean of two numbers. text{HM}(A, B) = 2/frac{1{A} + 1/B} = 1/3 So 1/A + 1/B = 6. text{HM}(C, D) = 2/frac{1{C} + 1/D} = 1/5 So 1/C + 1/D = 10. Step 2: Compute HM of all four values A, B, C, D. text{HM}(A,B,C,D) = 4/frac{1{A} + 1/B + 1/C + 1/D} = 4/6 + 10 = 4/16 = 1/4 Hence, Option B is the correct answer.

The harmonic mean $A$ and $B$ is $1/3$ and harmonic mean of $C$ and $D$ is $1/5$. The harmonic mean of $ABCD$ is

The correct answer is Option b: $1/4$. **Step 1: Recall the formula for Harmonic Mean of two numbers.** $$\text{HM}(A, B) = \frac{2}{\frac{1}{A} + \frac{1}{B}} = \frac{1}{3}$$ So $\frac{1}{A} + \frac{1}{B} = 6$. $$\text{HM}(C, D) = \frac{2}{\frac{1}{C} + \frac{1}{D}} = \frac{1}{5}$$ So $\frac{1}{C} + \frac{1}{D} = 10$. **Step 2: Compute HM of all four values A, B, C, D.** $$\text{HM}(A,B,C,D) = \frac{4}{\frac{1}{A} + \frac{1}{B} + \frac{1}{C} + \frac{1}{D}} = \frac{4}{6 + 10} = \frac{4}{16} = \frac{1}{4}$$ Hence, **Option B** is the correct answer.

Central Tendency & DispersionPYQ Nov. 20Question 3001 of 473

All Questions

The harmonic mean $\displaystyle A$ and $\displaystyle B$ is $\displaystyle 1/3$ and harmonic mean of $\displaystyle C$ and $\displaystyle D$ is $\displaystyle 1/5$ . The harmonic mean of $\displaystyle ABCD$ is

Options

\displaystyle 8/15

\displaystyle 1/4

\displaystyle 1/15

\displaystyle 5/3

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Correct Answer

✅ Option b — $\displaystyle 1/4$

All Options:

A $\displaystyle 8/15$
B $\displaystyle 1/4$
C $\displaystyle 1/15$
D $\displaystyle 5/3$

Detailed Solution & Explanation

**Step 1: Recall the formula for Harmonic Mean of two numbers.**

\text{HM}(A, B) = \frac{2}{\frac{1}{A} + \frac{1}{B}} = \frac{1}{3}

\displaystyle \frac{1}{A} + \frac{1}{B} = 6

\text{HM}(C, D) = \frac{2}{\frac{1}{C} + \frac{1}{D}} = \frac{1}{5}

\displaystyle \frac{1}{C} + \frac{1}{D} = 10

. **Step 2: Compute HM of all four values A, B, C, D.**

\text{HM}(A,B,C,D) = \frac{4}{\frac{1}{A} + \frac{1}{B} + \frac{1}{C} + \frac{1}{D}} = \frac{4}{6 + 10} = \frac{4}{16} = \frac{1}{4}

Hence, **Option B** is the correct answer.

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The harmonic mean A\displaystyle AA and B\displaystyle BB is 1/3\displaystyle 1/31/3 and harmonic mean of C\displaystyle CC and D\displaystyle DD is 1/5\displaystyle 1/51/5. The harmonic mean of ABCD\displaystyle ABCDABCD is