The product of two consecutive even positive numbers is 728. What is the larger number?
Answer and explanation
Correct answer: 28
Let the smaller consecutive even number be x. The next consecutive even number is x + 2, not x + 1, because even numbers differ by 2. The product condition becomes x(x + 2) = 728, or x² + 2x − 728 = 0. Factoring gives (x − 26)(x + 28) = 0, so x = 26 or x = −28. Since the numbers are positive, x = 26. The larger number is therefore x + 2 = 28, making option C correct. Verification is 26 × 28 = 728. Options A, B, and D do not represent the larger member of a positive consecutive-even pair whose product is 728; in particular, 24 × 26 = 624 and 28 × 30 = 840.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
Let the smaller consecutive even number be x. The next consecutive even number is x + 2, not x + 1, because even numbers differ by 2. The product condition becomes x(x + 2) = 728, or x² + 2x − 728 = 0. Factoring gives (x − 26)(x + 28) = 0, so x = 26 or x = −28. Since the numbers are positive, x = 26. The larger number is therefore x + 2 = 28, making option C correct. Verification is 26 × 28 = 728. Options A, B, and D do not represent the larger member of a positive consecutive-even pair whose product is 728; in particular, 24 × 26 = 624 and 28 × 30 = 840.
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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