The product of two consecutive positive odd integers is 195. What is the smaller integer?

Correct answer: 13

This is a word problem modeled by a quadratic equation. Let the smaller positive odd integer be n. The next consecutive odd integer is n + 2, so n(n + 2) = 195, giving n² + 2n − 195 = 0. Factoring, (n + 15)(n − 13) = 0, so n = 13 or n = −15. Because the question requires positive integers, n = −15 must be rejected. Direct verification confirms that 13 × 15 = 195, and 13 and 15 are consecutive odd integers. Thus the smaller integer is 13. Option B is the larger member of the pair, while 11 and 17 do not form a consecutive odd pair whose product is 195.