What are the two consecutive positive odd integers whose product is 483?

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21 and 22

21 and 23

22 and 24

23 and 26

answer is B.

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Detailed Solution

Given that 483 is the product of the two consecutive positive odd integers.
Let the consecutive positive odd numbers be

x and x + 2

.
Therefore,

⇒ x (x + 2) = 483 ⇒ x 2 + 2 x = 483 ⇒ x 2 + 2 x − 483 = 0

Factoring the equation,

x 2 + 23 x − 21 x − 483 = 0 ⇒ x (x + 23) − 21 (x + 23) ⇒ (x + 23) (x − 21) = 0

Solve for x,

∴ (x + 23) = 0 ⇒ x = − 23

∴ (x − 21) = 0 ⇒ x = 21

We know that

x

should be a positive odd integer. Hence,

x = 21

Substituting the

x = 21 in x + 2 :

= 21 + 2 = 23

Hence, the required consecutive numbers are

21 and 23

.
Therefore, option 2 is correct.

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