Question

The product of two consecutive positive integers is 272. What is the larger of the two integers?

• A. 17
• B. 16
• C. 18
• D. 19
• E. 15

Hint:

For consecutive integers, always set them as \(n, n+1\). It reduces the problem to a quadratic equation.

Answer 1

The Correct Option is C

Step 1: Let the integers be \(n\) and \(n+1\).
Their product is \(n(n+1) = 272\).
Step 2: Solve quadratic.
\(n^2+n-272=0\).
Discriminant \(D = 1 + 4 \cdot 272 = 1089\).
\(\sqrt{1089} = 33\).
Step 3: Roots.
\(n = \frac{-1 \pm 33}{2}\).
Positive solution: \(n = \frac{32}{2} = 16\).
Step 4: Larger integer.
If \(n=16\), then larger = \(17\). But check product: \(16 \times 17 = 272\). Yes correct. So larger integer = 17. Final Answer: \[ \boxed{17} \]