If the product of three consecutive numbers is 210 then sum of the smaller numbers is

Options

A. 3
B. 4
C. 5
D. 11

Answer

To solve the problem step by step, we need to find three consecutive numbers whose product is 210 and then calculate the sum of the two smaller numbers.

### Step 1: Understand the Problem
We need to find three consecutive numbers such that their product equals 210. Let's denote these numbers as \( n-1 \), \( n \), and \( n+1 \) where \( n \) is the middle number.

### Step 2: Set Up the Equation
The product of the three consecutive numbers can be expressed as:
\[ (n-1) \times n \times (n+1) = 210 \]

### Step 3: Estimate the Middle Number
To find \( n \), we can estimate the cube root of 210 to get an approximate value for \( n \):
\[ \sqrt[3]{210} \approx 6 \]
This suggests that \( n \) is around 6.

### Step 4: Identify the Consecutive Numbers
Using \( n = 6 \):
- The three consecutive numbers are \( 5 \) (which is \( n-1 \)), \( 6 \) (which is \( n \)), and \( 7 \) (which is \( n+1 \)).

### Step 5: Verify the Product
Now, let's verify the product:
\[ 5 \times 6 \times 7 = 30 \times 7 = 210 \]
This confirms that the three consecutive numbers are indeed \( 5 \), \( 6 \), and \( 7 \).

### Step 6: Calculate the Sum of the Two Smaller Numbers
Now, we need to find the sum of the two smaller numbers:
\[ 5 + 6 = 11 \]

### Final Answer
The sum of the two smaller numbers is \( 11 \).

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