Measures of Central Tendency and DispersionPYQ Jan 26Question 4213 of 473
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If the arithmetic mean of two numbers is 13 and the geometric mean is 12, then the difference between the two numbers is:

Options

A8
B10
C12
D14
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Correct Answer

✅ Option b — 10

All Options:

  • A8
  • B10
  • C12
  • D14

Detailed Solution & Explanation

Let the two numbers be a\displaystyle a and b\displaystyle b.

Given:
1) Arithmetic Mean (AM) = 13\displaystyle 13
a+b2=13  ⟹  a+b=26\frac{a + b}{2} = 13 \implies a + b = 26 ---(Equation 1)
2) Geometric Mean (GM) = 12\displaystyle 12
ab=12  ⟹  ab=122=144\sqrt{ab} = 12 \implies ab = 12^2 = 144 ---(Equation 2)

We need to find the absolute difference between the two numbers, i.e., ∣a−b∣\displaystyle |a - b|. Using the algebraic identity:
(a−b)2=(a+b)2−4ab(a - b)^2 = (a + b)^2 - 4ab
Substitute the values from Equation 1 and Equation 2:
(a−b)2=(26)2−4(144)(a - b)^2 = (26)^2 - 4(144)(a−b)2=676−576(a - b)^2 = 676 - 576
(a−b)2=100(a - b)^2 = 100
Taking the square root on both sides:
∣a−b∣=100=10|a - b| = \sqrt{100} = 10

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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