Measures of Central Tendency and DispersionMCQPYQ Nov 24Question 3029 of 473
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If the AM & GM of two numbers are 30\displaystyle 30 and 24\displaystyle 24 respectively. Find the no's.

Options

A12\displaystyle 12 and 24\displaystyle 24
B48\displaystyle 48 and 12\displaystyle 12
C30\displaystyle 30 and 20\displaystyle 20
D40\displaystyle 40 and 20\displaystyle 20
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Correct Answer

✅ Option b — 48\displaystyle 48 and 12\displaystyle 12

All Options:

  • A12\displaystyle 12 and 24\displaystyle 24
  • B48\displaystyle 48 and 12\displaystyle 12
  • C30\displaystyle 30 and 20\displaystyle 20
  • D40\displaystyle 40 and 20\displaystyle 20

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Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be a\displaystyle a and b\displaystyle b. a+b2=30⇒a+b=60\frac{a+b}{2} = 30 \Rightarrow a + b = 60 ab=24⇒ab=576\sqrt{ab} = 24 \Rightarrow ab = 576 **Step 2: Solve for a\displaystyle a and b\displaystyle b.** (a−b)2=(a+b)2−4ab=3600−2304=1296\displaystyle (a-b)^2 = (a+b)^2 - 4ab = 3600 - 2304 = 1296 ∣a−b∣=36|a-b| = 36 From a+b=60\displaystyle a + b = 60 and a−b=36\displaystyle a - b = 36: 2a=96⇒a=48,b=122a = 96 \Rightarrow a = 48, \quad b = 12 **Verification:** - AM = (48+12)/2=30\displaystyle (48+12)/2 = 30 ✓ - GM = 48×12=576=24\displaystyle \sqrt{48 \times 12} = \sqrt{576} = 24 ✓ So the numbers are 48\displaystyle 48 and 12\displaystyle 12 = **Option B**. Note: The exam key says D (40\displaystyle 40 and 20\displaystyle 20), but AM of 40 and 20 = 30 ✓, GM = 800≠24\displaystyle \sqrt{800} \neq 24. The correct answer is **B** (48\displaystyle 48 and 12\displaystyle 12). 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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