Find the numbers whose GM is 5 and AM is 7.5 :

Option b: 13.09 and 1.91. Solution: Step 1: Set up equations. Let the two numbers be a and b . a+b/2 = 7.5 ⟹ a + b = 15 sqrt(ab) = 5 ⟹ ab = 25 Step 2: Solve the quadratic. (a-b)2 = (a+b)2 - 4ab = 225 - 100 = 125 |a-b| = sqrt(125) = 5sqrt(5) ≈ 11.18 From a + b = 15 and a - b = 11.18 : a = 15 + 11.18/2 = 26.18/2 ≈ 13.09 b = 15 - 11.18/2 = 3.82/2 ≈ 1.91 Verification: - AM = (13.09 + 1.91)/2 = 15/2 = 7.5 ✓ - GM = sqrt(13.09 × 1.91) = sqrt(25) = 5 ✓ Hence, Option B is the correct answer.

Find the numbers whose GM is $5$ and AM is $7.5$:

The correct answer is Option b: $13.09$ and $1.91$. **Step 1: Set up equations.** Let the two numbers be $a$ and $b$. $$\frac{a+b}{2} = 7.5 \Rightarrow a + b = 15$$ $$\sqrt{ab} = 5 \Rightarrow ab = 25$$ **Step 2: Solve the quadratic.** $$(a-b)^2 = (a+b)^2 - 4ab = 225 - 100 = 125$$ $$|a-b| = \sqrt{125} = 5\sqrt{5} \approx 11.18$$ From $a + b = 15$ and $a - b = 11.18$: $$a = \frac{15 + 11.18}{2} = \frac{26.18}{2} \approx 13.09$$ $$b = \frac{15 - 11.18}{2} = \frac{3.82}{2} \approx 1.91$$ **Verification:** - AM = $(13.09 + 1.91)/2 = 15/2 = 7.5$ ✓ - GM = $\sqrt{13.09 \times 1.91} = \sqrt{25} = 5$ ✓ Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IQuestion 3066 of 473

All Questions

Find the numbers whose GM is $\displaystyle 5$ and AM is $\displaystyle 7.5$ :

Options

\displaystyle 12

and

\displaystyle 13

\displaystyle 13.09

and

\displaystyle 1.91

\displaystyle 14

and

\displaystyle 11

\displaystyle 17

and

\displaystyle 19

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

Correct Answer

✅ Option b — $\displaystyle 13.09$ and $\displaystyle 1.91$

All Options:

A $\displaystyle 12$ and $\displaystyle 13$
B $\displaystyle 13.09$ and $\displaystyle 1.91$
C $\displaystyle 14$ and $\displaystyle 11$
D $\displaystyle 17$ and $\displaystyle 19$

Detailed Solution & Explanation

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

\displaystyle a

and

\displaystyle b

\frac{a+b}{2} = 7.5 \Rightarrow a + b = 15

\sqrt{ab} = 5 \Rightarrow ab = 25

**Step 2: Solve the quadratic.**

(a-b)^2 = (a+b)^2 - 4ab = 225 - 100 = 125

|a-b| = \sqrt{125} = 5\sqrt{5} \approx 11.18

From

\displaystyle a + b = 15

and

\displaystyle a - b = 11.18

a = \frac{15 + 11.18}{2} = \frac{26.18}{2} \approx 13.09

b = \frac{15 - 11.18}{2} = \frac{3.82}{2} \approx 1.91

**Verification:** - AM =

\displaystyle (13.09 + 1.91)/2 = 15/2 = 7.5

✓ - GM =

\displaystyle \sqrt{13.09 \times 1.91} = \sqrt{25} = 5

✓ Hence, **Option B** 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 numbers whose GM is 5\displaystyle 55 and AM is 7.5\displaystyle 7.57.5: