The product of two consecutive positive integers is 210. What is the larger integer?
Answer and explanation
Correct answer: 15
The governing concept is translating consecutive integers into algebraic expressions. Let the smaller positive integer be x; then the larger one is x + 1. The condition gives x(x + 1) = 210, so x² + x − 210 = 0. Factoring gives (x + 15)(x − 14) = 0, producing x = 14 or x = −15. Since the integers are positive, x = 14 is valid and the larger integer is x + 1 = 15. Therefore option C is correct. Checking directly, 14 × 15 = 210. Options A, B, and D do not form the required consecutive pair with product 210; in particular, 14 is the smaller integer, not the larger one.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The governing concept is translating consecutive integers into algebraic expressions. Let the smaller positive integer be x; then the larger one is x + 1. The condition gives x(x + 1) = 210, so x² + x − 210 = 0. Factoring gives (x + 15)(x − 14) = 0, producing x = 14 or x = −15. Since the integers are positive, x = 14 is valid and the larger integer is x + 1 = 15. Therefore option C is correct. Checking directly, 14 × 15 = 210. Options A, B, and D do not form the required consecutive pair with product 210; in particular, 14 is the smaller integer, not the larger one.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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