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 ⟹ a + b = 20 sqrt(ab) = 6 ⟹ 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, b = 2 Verification: - AM = (18+2)/2 = 10 ✓ - GM = sqrt(18 × 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 ≠ 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.

Measures of Central Tendency and DispersionMCQMTP 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

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

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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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