Question

The sum of three consecutive integers is $24$. Find the product of the integers.

• A. $504$
• B. $720$
• C. $540$
• D. none of these

Answer 1

The correct option is A

$504$

Step 1: Explanation for correct answer

Option (a): $504$

Let the three consecutive integers be $x,x+1$ and$x+2$

It is given that the sum of the integers is $24$, therefore, we have:

$\begin{array}{r}x+(x+1)+(x+2)=24\end{array}$

$\begin{array}{rcl}x+x+1+x+2& =& 24\\ x+x+1+x+2& =& 24\\ 3x+3& =& 24\\ 3x& =& 24-3\\ 3x& =& 21\\ x& =& \frac{21}{3}\\ x& =& 7\end{array}$

Step 2: Substitute the value of $x$

Therefore, $x=7$ and the other two integers are:

$$\begin{gathered} x+1=7+1 \\ x+1=8 \end{gathered}$$ and

$$\begin{gathered} x+2=7+2 \\ x+2=9 \end{gathered}$$

Now, we find the product of the integers as shown below:

$$\begin{gathered} x(x+1)(x+2)=7\times 8\times 9 \\ x(x+1)(x+2)=504 \end{gathered}$$

Thus, the product of the integers is $504$.

Therefore, option (a) is the correct answer.

Step 3: Explanation for the incorrect answers

Option (b): $720$

Option (c): $540$

Option (d): none of these

Thus, by calculating of the product of the integers, we get $504$.

Therefore, option (b), (c) and (d) are incorrect answers.

Hence, option (a) is the correct answer.