The difference between two numbers is 11 and their product is 672. What is the larger number?
Answer and explanation
Correct answer: 32
Let the smaller number be x. Because the difference is 11, the larger number is x + 11. Their product condition gives x(x + 11) = 672, so x² + 11x − 672 = 0. This factors as (x − 21)(x + 32) = 0. Thus x = 21 or x = −32. Under the intended positive-number interpretation, the smaller number is 21 and the larger number is 21 + 11 = 32. Hence option D is correct. Substitution verifies the answer: 21 × 32 = 672 and 32 − 21 = 11. Option A is the smaller number, not the larger one; options B and C do not form a pair with difference 11 and product 672. The governing skill is choosing variables according to the stated difference and rejecting the irrelevant negative root.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Let the smaller number be x. Because the difference is 11, the larger number is x + 11. Their product condition gives x(x + 11) = 672, so x² + 11x − 672 = 0. This factors as (x − 21)(x + 32) = 0. Thus x = 21 or x = −32. Under the intended positive-number interpretation, the smaller number is 21 and the larger number is 21 + 11 = 32. Hence option D is correct. Substitution verifies the answer: 21 × 32 = 672 and 32 − 21 = 11. Option A is the smaller number, not the larger one; options B and C do not form a pair with difference 11 and product 672. The governing skill is choosing variables according to the stated difference and rejecting the irrelevant negative root.
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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