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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Question : If the product of three consecutive numbers is 210, then the sum of the 2 smaller numbers is:
Option 2: 4
Option 3: 5
Question : The sum of three consecutive natural numbers divisible by 3 is 45. The smallest number is:
Option 1: 18
Option 2: 3
Option 3: 12
Option 4: 9
Question : If the square of the sum of two numbers is equal to 4 times their product, then the ratio of these numbers is:
Option 1: 2 : 1
Option 2: 1 : 3
Option 3: 1 : 1
Option 4: 1 : 2
Question : If the sum of two numbers is 60 and their HCF and LCM are 5 and 60, respectively, then the sum of the reciprocals of the numbers will be:
Option 1: $\frac{1}{11}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{1}{5}$
Question : Three numbers are in the ratio 5 : 6 : 7. If the product of the number is 5670, then the greatest number is:
Option 1: 15
Option 2: 18
Option 3: 21
Option 4: 28
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