Home › CAT › quantitativeaptitude › Sequences and Series › The Geometric Mean (GM) of $4$ and $9$ is
The 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: NCERT Class 11 Mathematics, Ch 8, §8.4 (Geometric Mean), p. 10._
Related questions
Sum of GP: 1 + 1/2 + 1/4 + ... to infinity =GP with first term 2, common ratio 3. Find 5th term.Sum of first 20 natural numbers:The 10th term of the AP 3, 7, 11, ... is:The AM-GM INEQUALITY for two POSITIVE numbers $a$ and $b$ states thatIf the AM and GM of two positive numbers are $5$ and $4$ respectively, the numbers areThree numbers are in AP. Their sum is $24$ and their product is $440$. Find the smallest oSum of the CUBES of the first $n$ natural numbers, $1^3 + 2^3 + \ldots + n^3$, equals