The product of two consecutive positive integers is 380. What is the larger integer?
Answer and explanation
Correct answer: 20
Let the smaller integer be \(x\), so the larger integer is \(x+1\). Thus, \(x(x+1)=380\), giving \(x^2+x-380=0\). Factoring gives \((x-19)(x+20)=0\). Since the integers are positive, \(x=19\), so the larger integer is \(20\). Option 19 is the smaller integer, not the required larger one. Exam tip: For consecutive integers, look for factor pairs whose difference is 1.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Let the smaller integer be \(x\), so the larger integer is \(x+1\). Thus, \(x(x+1)=380\), giving \(x^2+x-380=0\). Factoring gives \((x-19)(x+20)=0\). Since the integers are positive, \(x=19\), so the larger integer is \(20\). Option 19 is the smaller integer, not the required larger one. Exam tip: For consecutive integers, look for factor pairs whose difference is 1.
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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