Question

Product of three consecutive odd numbers is 1716. What is the largest of three numbers?
(A) 9
(B) 11
(C) 13
(D) None of these

Answer 1

Hint: Take the three numbers as x, x\[ + \]2, x\[ + \]4 where x is an odd number and then use the information given in the question to form an equation and from there find x.
The product of three consecutive odd numbers is odd.

Complete step-by-step solution:
The product of three consecutive odd numbers is odd.
It can be verified as,
Consecutive numbers make a sequence where each number is one more than the previous number.
For an odd consecutive number if x is an odd number, then the next consecutive odd number is x\[ + \]2.
Then the next consecutive odd number after x\[ + \]2 is x\[ + \]4.
So, let the numbers be x, x\[ + \]2, x\[ + \]4 .
According to the question, the product of them is 1716 .
Therefore,
\[x \times (x + 2) \times (x + 4) = 1716\] ……(1)
AS, 1716 \[ = \]2 \[ \times \]2 \[ \times \]3 \[ \times \]11 \[ \times \]13
\[ = \] 11\[ \times \]12\[ \times \]13
It is possible as the left hand side of (1) is a product of odds and the right hand side of (1) has 11 and 13 as odd but 12 is not odd.
So, here the product of three consecutive odd numbers is 1716 which is even.
So, it is not possible.
Hence, option (D) is correct.

Note: Students should notice the question carefully as it is a trick question. Don’t calculate it by the usual method to find x. Many students waste their time in calculating. Just use the fact that the product of three consecutive odd numbers is odd. If the odd term is not mentioned in the question then students must follow the usual method as shown above. In that case one should consider the numbers as x, x\[ + \]1, x\[ + \]2. For even consecutive numbers the numbers should be considered as x,
 x\[ + \]2, x\[ + \]4 where x is an even number.