Find the two numbers if AM and GM is 10 and 6 respectively.

Option d: 18, 2. Solution: Step 1: Set up equations. Let the two numbers be a and b. a+b/2 = 10 Rightarrow a + b = 20 sqrt(ab) = 6 Rightarrow ab = 36 Step 2: Solve. (a-b)^2 = (a+b)^2 - 4ab = 400 - 144 = 256 |a-b| = 16 From a + b = 20 and a - b = 16: a = 18, quad b = 2 Verification: - AM = (18+2)/2 = 10 ✓ - GM = sqrt(18 x 2) = sqrt(36) = 6 ✓ The numbers are 18 and 2 = Option D. Note: The exam key says C (9, 4) but: AM of 9,4 = 6.5 !=q 10. The correct answer is D (18, 2). Hence, Option D is the correct answer.

Find the two numbers if AM and GM is $10$ and $6$ respectively.

The correct answer is Option d: $18, 2$. **Step 1: Set up equations.** Let the two numbers be $a$ and $b$. $$\frac{a+b}{2} = 10 \Rightarrow a + b = 20$$ $$\sqrt{ab} = 6 \Rightarrow ab = 36$$ **Step 2: Solve.** $$(a-b)^2 = (a+b)^2 - 4ab = 400 - 144 = 256$$ $$|a-b| = 16$$ From $a + b = 20$ and $a - b = 16$: $$a = 18, \quad b = 2$$ **Verification:** - AM = $(18+2)/2 = 10$ ✓ - GM = $\sqrt{18 \times 2} = \sqrt{36} = 6$ ✓ The numbers are $18$ and $2$ = **Option D**. Note: The exam key says C ($9, 4$) but: AM of $9,4$ = $6.5 \neq 10$. The correct answer is **D** ($18, 2$). Hence, **Option D** is the correct answer.

Central Tendency & DispersionMTP Nov 21Question 3060 of 473

All Questions

Find the two numbers if AM and GM is $\displaystyle 10$ and $\displaystyle 6$ respectively.

Options

\displaystyle 6, 6

\displaystyle 12, 8

\displaystyle 9, 4

\displaystyle 18, 2

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Correct Answer

✅ Option d — $\displaystyle 18, 2$

All Options:

A $\displaystyle 6, 6$
B $\displaystyle 12, 8$
C $\displaystyle 9, 4$
D $\displaystyle 18, 2$

Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be

\displaystyle a

and

\displaystyle b

\frac{a+b}{2} = 10 \Rightarrow a + b = 20

\sqrt{ab} = 6 \Rightarrow ab = 36

**Step 2: Solve.**

(a-b)^2 = (a+b)^2 - 4ab = 400 - 144 = 256

|a-b| = 16

From

\displaystyle a + b = 20

and

\displaystyle a - b = 16

a = 18, \quad b = 2

**Verification:** - AM =

\displaystyle (18+2)/2 = 10

✓ - GM =

\displaystyle \sqrt{18 \times 2} = \sqrt{36} = 6

✓ The numbers are

\displaystyle 18

and

\displaystyle 2

= **Option D**. Note: The exam key says C (

\displaystyle 9, 4

) but: AM of

\displaystyle 9,4

\displaystyle 6.5 \neq 10

. The correct answer is **D** (

\displaystyle 18, 2

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

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Find the two numbers if AM and GM is 10\displaystyle 1010 and 6\displaystyle 66 respectively.