Central Tendency & DispersionPYQ Dec 23Question 3041 of 473
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If A.M and G.M of two positive numbers a\displaystyle a and b\displaystyle b are 12 and 12, respectively, find the numbers

Options

A18 and 6
B15 and 9
C16 and 8
D12 and 12
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Correct Answer

✅ Option d — 12 and 12

All Options:

  • A18 and 6
  • B15 and 9
  • C16 and 8
  • D12 and 12

Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be a\displaystyle a and b\displaystyle b. a+b2=12⇒a+b=24\frac{a+b}{2} = 12 \Rightarrow a + b = 24 ab=12⇒ab=144\sqrt{ab} = 12 \Rightarrow ab = 144 **Step 2: Solve the quadratic.** (a−b)2=(a+b)2−4ab=576−576=0(a-b)^2 = (a+b)^2 - 4ab = 576 - 576 = 0 a−b=0⇒a=ba - b = 0 \Rightarrow a = b From a+b=24\displaystyle a + b = 24: 2a=24⇒a=12,b=122a = 24 \Rightarrow a = 12, \quad b = 12 **Step 3: Verify.** - AM = (12+12)/2 = 12 ✓ - GM = √(12×12) = 12 ✓ The numbers are 12 and 12 (equal). This makes sense because AM = GM only when all values are equal. Hence, **Option D** is the correct answer.

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