Central Tendency & DispersionMTP Nov 18Question 3050 of 473
All Questions

Relationship between AM, GM, and HM

Options

AAM≥GM≥HM\displaystyle AM \geq GM \geq HM
BAM≥GM≤HM\displaystyle AM \geq GM \leq HM
CHM≥AM≥GM\displaystyle HM \geq AM \geq GM
Dnone of these
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Correct Answer

✅ Option a — AM≥GM≥HM\displaystyle AM \geq GM \geq HM

All Options:

  • AAM≥GM≥HM\displaystyle AM \geq GM \geq HM
  • BAM≥GM≤HM\displaystyle AM \geq GM \leq HM
  • CHM≥AM≥GM\displaystyle HM \geq AM \geq GM
  • Dnone of these

Detailed Solution & Explanation

**Step 1: Recall the standard inequality between AM, GM, and HM.** For any set of positive real numbers, the following inequality always holds: AM≥GM≥HM\text{AM} \geq \text{GM} \geq \text{HM} with equality if and only if all values are equal. **Step 2: Evaluate the options.** - Option A: AM≥GM≥HM\displaystyle AM \geq GM \geq HM — this is the **correct** mathematical inequality. - Option C: HM≥AM≥GM\displaystyle HM \geq AM \geq GM — this is incorrect (reverses the inequality). **Conclusion:** The correct relationship is AM ≥ GM ≥ HM, which is **Option A**. Note: The exam key says C, but that's mathematically wrong. The correct answer is A. Hence, **Option A** is the correct answer.

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