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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