Multiple choice

The product of two consecutive odd positive integers is 483. The integers are

  1. 21 and 23

  2. 27 and 29

  3. 17 and 19

  4. 31 and 33
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A Correct answer
Explanation

Let the two consecutive odd positive integers be x and x + 2. x(x + 2) = 483 $\Rightarrow$ x2 + 2x - 483 = 0 x2 + 23 x - 21 x  - 483 = 0 $\Rightarrow$ x (x + 23) - 21 (x + 23) = 0 (x + 23) (x - 21) = 0 x = -23 , x - 21 => x = 21. Since integers are positive, -23 can't be the answer. So, the two integers are 21 and 23.

AI explanation

Two consecutive odd integers can be written as x and x+2. Setting x(x+2) = 483 gives x² + 2x – 483 = 0, which factors to (x–21)(x+23)=0, so x = 21. The two consecutive odd integers are therefore 21 and 23, and indeed 21×23 = 483.

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