The product of two consecutive positive even integers is 168. What is the larger integer?
Answer and explanation
Correct answer: 14
Let the smaller even integer be x. The next consecutive even integer is x + 2. Thus, x(x + 2) = 168, giving x² + 2x − 168 = 0 = (x − 12)(x + 14). Since the integers are positive, x = 12, so the larger integer is 12 + 2 = 14. Exam tip: consecutive even integers always differ by 2.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Let the smaller even integer be x. The next consecutive even integer is x + 2. Thus, x(x + 2) = 168, giving x² + 2x − 168 = 0 = (x − 12)(x + 14). Since the integers are positive, x = 12, so the larger integer is 12 + 2 = 14. Exam tip: consecutive even integers 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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