Central Tendency & DispersionPYQ June 24Question 3006 of 473
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If the arithmetic mean of two numbers is 10\displaystyle 10 and the geometric mean is 6\displaystyle 6, then the difference in the numbers is

Options

A12
B14
C16
D8
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Correct Answer

✅ Option c — 16

All Options:

  • A12
  • B14
  • C16
  • D8

Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be a\displaystyle a and b\displaystyle b. AM=a+b2=10⇒a+b=20\text{AM} = \frac{a+b}{2} = 10 \Rightarrow a + b = 20 GM=ab=6⇒ab=36\text{GM} = \sqrt{ab} = 6 \Rightarrow ab = 36 **Step 2: Find the difference.** Using the identity: (a−b)2=(a+b)2−4ab=400−144=256(a - b)^2 = (a + b)^2 - 4ab = 400 - 144 = 256 ∣a−b∣=256=16|a - b| = \sqrt{256} = 16 Hence, **Option C** is the correct answer.

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