The product of two consecutive odd numbers is \(399\). What is the larger number?
Answer and explanation
Correct answer: 21
Let the smaller odd number be \(x\). The next consecutive odd number is therefore \(x+2\). Thus, \(x(x+2)=399\), giving \(x^2+2x-399=0\). Factoring, \((x-19)(x+21)=0\), so the positive value is \(x=19\), and the larger number is \(19+2=21\). Option 19 is the smaller number, not the larger one. Exam tip: consecutive odd numbers always differ by 2.
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
Let the smaller odd number be \(x\). The next consecutive odd number is therefore \(x+2\). Thus, \(x(x+2)=399\), giving \(x^2+2x-399=0\). Factoring, \((x-19)(x+21)=0\), so the positive value is \(x=19\), and the larger number is \(19+2=21\). Option 19 is the smaller number, not the larger one. Exam tip: consecutive odd numbers always differ by 2.
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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