Central Tendency & DispersionPYQ Dec 22Question 3035 of 473
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If Arithmetic Mean and Geometric Mean between two numbers are 5 and 4 respectively, then these two numbers are:

Options

A2 & 3
B2 & 8
C4 & 6
D1 & 16
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Correct Answer

✅ Option b — 2 & 8

All Options:

  • A2 & 3
  • B2 & 8
  • C4 & 6
  • D1 & 16

Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be a\displaystyle a and b\displaystyle b. a+b2=5⇒a+b=10\frac{a+b}{2} = 5 \Rightarrow a + b = 10 ab=4⇒ab=16\sqrt{ab} = 4 \Rightarrow ab = 16 **Step 2: Solve for a and b.** (a−b)2=(a+b)2−4ab=100−64=36(a-b)^2 = (a+b)^2 - 4ab = 100 - 64 = 36 ∣a−b∣=6|a-b| = 6 From a+b=10\displaystyle a + b = 10 and a−b=6\displaystyle a - b = 6: 2a=16⇒a=8,b=22a = 16 \Rightarrow a = 8, \quad b = 2 **Verification:** - AM = (8+2)/2=5\displaystyle (8+2)/2 = 5 ✓ - GM = 8×2=16=4\displaystyle \sqrt{8 \times 2} = \sqrt{16} = 4 ✓ Hence, **Option B** is the correct answer.

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