alleryThe Geometric Mean (GM) of $4$ and $9$ is
A$6.5$
B$5$
C$6$
D$36$
Answer & Solution
Correct answer: C. $6$
1. GM of two positive numbers $a, b$: $\text{GM} = \sqrt{ab}$.
2. Plug in $a = 4$, $b = 9$: $\text{GM} = \sqrt{36} = 6$.
3. Note: AM = $(4+9)/2 = 6.5$ and HM = $2\cdot 4 \cdot 9 / 13 = 72/13 \approx 5.54$. So AM > GM > HM (always true for distinct positives).
4. Option A is the AM (confusing the two). Option B is the HM (off but close). Option D is the PRODUCT $a \cdot b$ (forgot to take the root).
_Source: syllabus Mathematics, Ch 8, §8.4 (Geometric Mean), p. 10._
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