Question

If A, G, and H are the arithmetic, geometric and harmonic means between 36 and 64 respectively.

Statement 1. The value of G is 48.

Statement 2. The value of A is 50.

Statement 3. The value of H is 46.

Which of the above statements is/are correct?

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. None of the above

Answer 1

Correct Answer - Option 1 : 1 and 2 only

Given:

If A, G, and H are the arithmetic, geometric and harmonic means between 36 and 64 respectively.

Formula Used:

Arithmetic Mean = (a + b)/2

Geometric Mean = √(a × b)

Harmonic Mean = (2 × a × b)/(a + b)

Where a, and b are first term and last term respectively.

Calculation:

Arithmetic Mean = (a + b)/2

⇒ (36 + 64)/2

⇒ 100/2

⇒ 50

Geometric Mean = √(a × b)

⇒ √(36 × 64)

⇒ √2304

⇒ 48

Harmonic Mean = (2 × a × b)/(a + b)

⇒ (2 × 36 × 64)/(36 + 64)

⇒ 4608/100

⇒ 46.08

∴ Only statement 1 and 2 are correct.