If A.M and G.M of two positive numbers a and b are 12 and 12, respectively, find the numbers

Option d: 12 and 12. Solution: Step 1: Set up equations. Let the two numbers be a and b . a+b/2 = 12 ⟹ a + b = 24 sqrt(ab) = 12 ⟹ ab = 144 Step 2: Solve the quadratic. (a-b)2 = (a+b)2 - 4ab = 576 - 576 = 0 a - b = 0 ⟹ a = b From a + b = 24 : 2a = 24 ⟹ a = 12, b = 12 Step 3: Verify. - AM = (12+12)/2 = 12 ✓ - GM = √(12×12) = 12 ✓ The numbers are 12 and 12 (equal). This makes sense because AM = GM only when all values are equal. Hence, Option D is the correct answer.

If A.M and G.M of two positive numbers $a$ and $b$ are 12 and 12, respectively, find the numbers

The correct answer is Option d: 12 and 12. **Step 1: Set up equations.** Let the two numbers be $a$ and $b$. $$\frac{a+b}{2} = 12 \Rightarrow a + b = 24$$ $$\sqrt{ab} = 12 \Rightarrow ab = 144$$ **Step 2: Solve the quadratic.** $$(a-b)^2 = (a+b)^2 - 4ab = 576 - 576 = 0$$ $$a - b = 0 \Rightarrow a = b$$ From $a + b = 24$: $$2a = 24 \Rightarrow a = 12, \quad b = 12$$ **Step 3: Verify.** - AM = (12+12)/2 = 12 ✓ - GM = √(12×12) = 12 ✓ The numbers are 12 and 12 (equal). This makes sense because AM = GM only when all values are equal. Hence, **Option D** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Dec 23Question 3041 of 473

All Questions

If A.M and G.M of two positive numbers $\displaystyle a$ and $\displaystyle b$ are 12 and 12, respectively, find the numbers

Options

A18 and 6

B15 and 9

C16 and 8

D12 and 12

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

Correct Answer

✅ Option d — 12 and 12

All Options:

A18 and 6
B15 and 9
C16 and 8
D12 and 12

Detailed Solution & Explanation

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

\displaystyle a

and

\displaystyle b

\frac{a+b}{2} = 12 \Rightarrow a + b = 24

\sqrt{ab} = 12 \Rightarrow ab = 144

**Step 2: Solve the quadratic.**

(a-b)^2 = (a+b)^2 - 4ab = 576 - 576 = 0

a - b = 0 \Rightarrow a = b

From

\displaystyle a + b = 24

2a = 24 \Rightarrow a = 12, \quad b = 12

**Step 3: Verify.** - AM = (12+12)/2 = 12 ✓ - GM = √(12×12) = 12 ✓ The numbers are 12 and 12 (equal). This makes sense because AM = GM only when all values are equal. 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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If A.M and G.M of two positive numbers a\displaystyle aa and b\displaystyle bb are 12 and 12, respectively, find the numbers