Question : If the product of three consecutive numbers is 210, then the sum of the smaller number is:
Option 1: 3
Option 2: 5
Option 3: 4
Option 4: 11
Correct Answer: 11
Solution :
Given that the product of three consecutive numbers is 210.
Let the three consecutive numbers as $(n-1)$, $n$, and $(n+1)$.
According to the question,
$n(n+1)(n-1) = 210$
$⇒n^3-n-210=0$
$⇒(n-6)(n^2+6n+35)=0$
$n = 6$ and $n \notin \mathrm{R}$
Therefore, the three consecutive numbers are 5, 6, and 7.
$\therefore$ The sum of the smaller number = 5 + 6 = 11
Hence, the correct answer is 11.
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