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 and $24 respectively. Find the no's.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — $48\displaystyle and $12

All Options:

  • A$12\displaystyle and $24
  • B$48\displaystyle and $12
  • C$30\displaystyle and $20
  • D$40\displaystyle and $20

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=60a+b2=30\displaystyle \frac{a+b}{2} = 30 \Rightarrow a + b = 60 ab=24⇒ab=576ab=24\displaystyle \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 48×12=576=24\displaystyle \sqrt{48 \times 12} = \sqrt{576} = 24 ✓ So the numbers are $48\displaystyle and $12 = **Option B**. Note: The exam key says D ($40\displaystyle and $20), but AM of 40 and 20 = 30 ✓, GM = 800≠24\displaystyle 800\displaystyle \sqrt{800} ≠\displaystyle \neq 24. The correct answer is **B** ($48\displaystyle and $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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