Question

Product of three consecutive odd numbers is $1287$. What is the largest of the three numbers?
A. 9
B. 11
C. 13
D. None of the above

Answer 1

Hint: Consecutive numbers are the numbers following each other continuously in a series or sequence. For Example: 27, 28, 29 are three consecutive numbers. And 27, 29, 31 are three consecutive odd numbers. In order to solve this question we will assume three consecutive odd numbers by using a variable. Then take their product as 1287 and solve the obtained equation to get the numbers. Then by comparing three obtained numbers we get the largest of the three, which is the required solution.

Complete step by step answer:
We have been given the product of three consecutive odd numbers as 1287. We have to find the largest of the three numbers. Some consecutive odd numbers are $1,3,5,7,9,11,13,......$
As we observed the above pattern there is a gap of 2 between two consecutive odd numbers. So let us assume that three consecutive odd numbers will be,
$\left( x-2 \right),x,\left( x+2 \right)$
Now, the product of these consecutive odd numbers is given as
\[\left( x-2 \right)x\left( x+2 \right)=1287\]
Now, we can write the number 1287 in the factored form as
$1287=9\times 11\times 13$
Substituting the value we will get
$\left( x-2 \right)x\left( x+2 \right)=9\times 11\times 13$
Now, when we compare both LHS and RHS we will get
$\left( x-2 \right)=9$
$\Rightarrow x=11$
$\therefore x+2=13$
The three consecutive odd numbers are $9,11,13$.
Therefore, The largest of the three numbers is 13. Hence, option (C) is correct.

Note: The key concept to solve this question is to write the factors of 1287. If we try to solve the product of variables, calculations become lengthy and the possibility of mistakes increases. Also remember that consecutive odd numbers have a gap of 2 between them, similarly consecutive even numbers have a gap of 2 between them.