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Question:

The product of two consecutive odd numbers is 399. What are the numbers?

A
19 and 21

Explaination

The fastest way to solve this would be to simply multiply the possible choices together (19 × 21 = 399). You can also solve this with algebra. Let x equal the first number and x + 2 the second number.

x(x + 2) = 399

x^{2} + 2x = 399 (Note: This is a quadratic equation that can be solved by setting it equal to zero and factoring.)

x^{2} + 2x – 399 = 0

(x – 19)(x + 21) = 0

x – 19 = 0 OR x + 21 = 0

x = 19 OR x = –21

x + 2 = 21 OR x + 2 = –19

Two solutions are possible: 19 and 21, and –21 and –19. Because the latter pair isn’t one of the answer choices, the first pair is the correct answer.